4.6 Physical Sciences
PHY421: Laser physics and advanced optics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Introduction
to
Lasers:
Principles
of
laser
action,
threshold
criteria,
building
blocks
of
a
laser,
Basic
properties
of
laser
light,
coherence,
directionality,
photon
flux,
Lasers
and
Masers,
Survey
of
laser
applications.

AtomField
interaction:
Einstein’s
A
and
B
coefficients,
Coherent
and
incoherent
emissions,
threelevel
and
four
level
schemes,
Rate
equation
model
for
laser,
Optical
pumping.

Gaussian
beam
and
Optical
resonators:
Propagation
of
Gaussian
beam,
ABCD
Matrix,
linear
and
ring
resonators,
Confocal
cavity,
stability
analysis
of
cavity,
cavity
modes,
quality
factor.

Types
of
Lasers:
Gas
lasers:
CO_{2}
and
Arion,
Liquid
dye
laser,
Solid
state
lasers
(Ruby
laser,
Nd:YAG),
semiconductor
lasers,
edge
emitting
and
vertical
cavity
surface
emitting
lasers,
Pulsed
laser
operation,
Qswitching,
saturable
absorption,
mode
locking,
Ultrafast
lasers.

Nonlinear
Optics:
Polarization
properties
of
lasers,
Jones
Matrix
formalism,
Nonlinear
effects,
second
harmonic
generation,
Kerr
effect,
Pockel
effect,
self
focusing
and
defocusing,
Optical
isolators.

Topics
in
Advanced
Optics:
Semiclassical
theory
of
laser,
Correlation
function
and
coherence
concepts,
Photon
statistics
in
cavities,
one
atom
laser,
Laser
cooling
and
trapping
of
atoms,
Introduction
to
optical
lattices
and
atom
optics.
Recommended Reading

A.
E.
Siegman,
Lasers,
University
Science
Books
(1986).

K.
K.
Sharma,
Optics,
Principles
and
applications,
Academic
Press
USA
(2006).

J.
T.
Verdeyen,
Laser
Electronics,
03rd
edition,
Prentice
Hall,
(1995).

K.
Thyagarajan
and
A.K.
Ghatak,
Lasers:
Theory
and
Applications,
Springer
(1981).

M.
Sargent
III,
M.O.
Scully
and
W.E.
Lamb,
Jr.,
Laser
Physics,
Westview
Press
(1978).

L.
Mandel
and
E.
Wolf,
Optical
Coherence
and
Quantum
Optics,
Cambridge
University
Press
(1995).

B. B. Laud,
Lasers
and
Nonlinear
Optics,
John
Wiley
&
Sons
Inc.
(1985).

C.
CohenTannoudji,
J.
DupontRoc,
and
G.
Grynberg,
AtomPhotonInteractions:
Basic
Processes
and
Applications,
WileyInterscience
NY
(1998).
PHY422: Computational methods in physics I


[Cr:4,
Lc:3,
Tt:0,
Lb:3]
Course Outline

Number
representation
in
computers,
round
off
error,
relative
error
estimation,
error
propagation.

Solution
of
Linear
Systems
AX = B:
Matrix
arithmetic,
Numerical
Diagonalization
of
matrices.
Singular
value
decomposition.
Eigenvalue
problem.
Gaussian
Elimination,
LU
Factorization,
Jacobi
and
GaussSeidel
method,
Error
estimation
and
Residual
Correction
method.

Interpolation:
Polynomial
interpolation,
Newton,
Lagrange
and
Hermite
interpolation,
spline
interpolation.

Numerical
Differentiation:
Differentiation
of
interpolating
polynomials,
Backward,
forward
and
centered
difference
methods,
method
of
undetermined
coefficients.

Numerical
Integration:
Trapezoidal
and
Composite
Trapezoidal,
Simpson’s
Rule,
Gaussian
quadrature,
Monte
Carlo
Integration.

Solution
of
Nonlinear
Equations
f(x) = 0:
Iteration,
Bracketing
methods
for
locating
a
root,
NewtonRaphson
and
Secant
methods.

Optimization:
Minimization,
minimization
in
several
dimensions,
Monte
Carlo
Markov
Chains
based
methods.
Metropolis
method,
convergence
of
Markov
Chains.
Recommended Reading

H.
M.
Antia,
Numerical
Methods
For
Scientists
And
Engineers,
02nd
edition,
Birkhauser
Basel
(2002).

Numerical
Recipes
in
C:
The
Art
of
Scientific
Computing,
W.
H.
Press,
S.
A.
Teukolsky,
W.
T.
Vellerling
and
B.
P.
Flannery,
Cambridge
University
Press
(1992).
PHY423: Mathematical methods for physicists II


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Fourier
series:
General
properties,
applications
of
Fourier
series,
properties
of
Fourier
series,
Gibbs
phenomenon,
discrete
Fourier
transform,
relation
with
fast
Fourier
transforms.

Integral
transforms:
Fourier
integral,
Fourier
transforms,
inversion
theorem,
Fourier
transform
of
derivatives,
convolution
theorem,
Laplace
transform
and
its
relation
to
Fourier
transform.
Laplace
transform
solution
to
differential
equations.
convolution
theorem,
Inverse
Laplace
transform.

Introduction
to
integral
equations:
Integral
transforms,
generating
functions,
Neumann
series,
separable
Kernels,
HilbertSchmidt
theory.

Calculus
of
Variations:
One
dependent
and
an
independent
variable,
Euler’s
equations,
several
dependent
variables,
several
independent
variables,
Lagrangian
multipliers,
variation
with
constraints.
Recommended Reading

H.
J.
Weber
and
G.
B.
Arfken,
Essential
Mathematical
Methods
for
Physicists,
Academic
Press
(2004).

D.
A.
McQuarrie,
Mathematical
Methods
for
Scientists
and
Engineers,
Viva
Books
(2009).

Mary
L.
Boas,
Mathematical
Methods
in
the
Physical
Sciences,
Wiley
(2005).
PHY424: Relativistic quantum mechanics and quantum field theory


[Cr:4,
Lc:4,
Tt:0,
Lb:0]
Goal: To trace the path from single particle Nonrelativistic Quantum Mechanics (QM)
to the necessity of many body interpretations of its relativistic generalizations.
Introduction of Quantum field theory as a comprehensive language to describe many
body relativistic quantum systems which resolves the paradoxes of single body
Relativistic QM.
Course Outline

Relativistic
Quantum
Mechanics:
KleinGordon
equation,
Dirac
equation
and
its
plane
wave
solutions,
significance
of
negative
energy
solutions,
spin
angular
momentum
of
the
Dirac
particle.
Nonrelativistic
limit
of
Dirac
equation,
Electron
in
electromagnetic
fields,
spin
magnetic
moment,
spinorbit
interaction.
Problems
of
relativistic
oneparticle
theories
and
the
need
for
QFT.

Classical
field
Theory:
Symmetries
and
Noether’s
theorem.
Stressenergy
tensor
and
propagator
theory
for
Schrodinger,
KleinGordon
and
Dirac
theories.

Relativistic
Quantum
Field
Theory:
Canonical
quantization
of
real
and
complex
scalar
fields.
Quantization
of
Spin
halffield.
Dirac,
Weyl
and
Majorana
fields.
Wick’s
theorem
for
spin
0,
1/2.
Heisenberg
and
Interaction
pictures
and
Perturbation
theory
for
correlation
functions.
Feynman
rules
for
correlators.
Spinstatistics
theorem
(noninteracting),
Causality.
Recommended Reading

J.
J.
Sakurai,
Advanced
Quantum
Mechanics,
(Pearson),
1967.

A.
Lahiri
and
P.
Pal,
A
First
Book
of
Quantum
Field
Theory,
(Narosa),
2007.

M.
Peskin
and
D.
Schroeder,
An
introduction
to
Quantum
Field
Theory,
(Westview
Press),
1995.

H.
Mandl
and
G.
Shaw,
Quantum
Field
Theory,
(WileyBlackwell),
2010.

M.
Srednicki,
Quantum
Field
Theory,
(Cambridge
University
Press),
2007.

L.
H.
Ryder,
Quantum
Field
Theory,
(Cambridge
University
Press),
1996.
PHY425: Computational methods in physics II


[Cr:4,
Lc:3,
Tt:0,
Lb:3]
Knowledge of the content of PHY422 is essential to follow this course.
Course Outline

Solution
of
Ordinary
Differential
Equations,
Euler’s
method,
RungeKutta
methods,
Initial
and
Boundary
Value
Problems.

Fast
Fourier
Transforms,
relation
with
Fourier
series
and
Fourier
transforms.

Partial
differential
equations:
Diffusion
equation,
Wave
equation,
Poisson
equation.
Finite
element
and
relaxation
methods.

Parallel
computing:
Decomposition
of
problems,
functional,
data
and
domain
decomposition.
Shared
memory
and
distributed
memory
parallelization.
Optimization
with
coprocessors
and
GPGPUs.
 Topics in Numerical Simulations (At least two topics to be covered):

Many
particle
simulations
with
short
range
interactions.

Many
particle
simulations
with
long
range
interactions.

Computational
Fluid
Dynamics.

Simulations
of
spin
systems.

Simulations
of
quantum
mechanical
scattering.

Parameter
estimation
for
n > 3
unknown
parameters
from
experimental/observational
data.
Recommended Reading

H.
M.
Antia,
Numerical
Methods
For
Scientists
And
Engineers,
02nd
edition,
Birkhauser
Basel
(2002).

Numerical
Recipes
in
C:
The
Art
of
Scientific
Computing,
W.
H.
Press,
S.
A.
Teukolsky,
W.
T.
Vellerling
and
B.
P.
Flannery,
Cambridge
University
Press
(1992).

Programming
Massively
Parallel
Processors:
A
Handson
Approach,
by
David
B.
Kirk,
Wenmei
W.
Hwu,
Publisher:
Morgan
Kaufmann;
3rd
edition
(2016)

Computational
Physics,
J.
M.
Thijssen,
Cambridge
University
Press
(1999)
PHY601: Review of classical mechanics


[Cr:4,
Lc:2,
Tt:2,
Lb:0]
Course Outline

Lagrangian
and
Hamiltonian
formulation
of
classical
mechanics,
two
body
central
force
problem,
rigid
body
motion,
special
theory
of
relativity,
phase
space
formulation
of
classical
mechanics.
Nonlinearity
and
chaos.
(The
methodology
of
the
course
will
be
based
on
learning
by
problem
solving)
Recommended Reading

H.
Goldstein,
Classical
mechanics,
03rd
edition,
AddisonWesley,
Cambridge
MA
(2001).

L.
D.
Landau
and
E.M.
Lifshitz,
Mechanics,
03rd
edition,
Butterworth
Heinemann
(1976).
PHY602: Review of electrodynamics


[Cr:4,
Lc:2,
Tt:2,
Lb:0]
Course Outline

Gauss
law,
Electrostatics,
boundary
value
problems,
Greens
function,
magnetostatics,
Electrodynamics,
Faraday’s
law,
Amperes
law,
Maxwell’s
equations,
covariant
form
of
Maxwell
equations,
electromagnetic
waves
and
their
propagation,
retarded
potentials,
radiation.
(The
course
will
be
based
on
learning
by
problem
solving)
Recommended Reading

J.
D.
Jackson,
Classical
Electrodynamics,
3rd
edition,
New
York:
Wiley.

D.
J.
Griffiths,
Introduction
to
Electrodynamics,
03rd
edition,
PrenticeHall
NJ
(1999).

L.
D.
Landau
and
E.M.
Lifshitz,
The
Classical
theory
of
fields,
4th
edition,
Pergamon
(1994).
PHY603: Review of statistical mechanics


[Cr:4,
Lc:2,
Tt:2,
Lb:0]
Course Outline

Review
of
thermodynamics.
Equation
of
state,
equilibrium
and
stability,
Van
der
Waal
gas,
phase
transitions,
Laws
of
thermodynamics.
Carnot
engine,
heat
pump.
Disorder
and
Entropy.
Phase
space.
Probability
density
and
functions
of
a
random
variable,
Liouville
Theorem.

Microcanonical
ensemble,
Boltzmann
probability.
Canonical
ensemble,
partition
function,
Monoatomic
ideal
gas,
virial
theorem,
energy
fluctuations,
collection
of
harmonic
oscillators,
statistics
of
paramagnetism,
polyatomic
gas.
Grand
canonical
ensemble,
density
and
energy
fluctuations.
Density
matrix
formalism.
Examples.

Quantum
statistics.
Indistinguishable
particles,
symmetric
vs
antisymmetric
wave
function.
Ideal
Bose
gas
and
ideal
Fermi
gas
in
quantum
ensembles
and
thermodynamic
properties,
Blackbody
radiation.
BoseEinstein
condensation.
Specific
heat
of
solids.
Pauli
paramagnetism.
Introduction
to
Phase
transitions.
Recommended Reading

R.
K.
Pathria,
Statistical
Mechanics,
02nd
edition,
ButterworthHeinemann
(1996).

K.
Huang,
Statistical
Mechanics,
02nd
edition,
Wiley
(1987).

L.
D.
Landau
and
E.
M.
Lifshitz,
Course
in
Theoretical
Physics
Vol.
5,
03rd
edition,
ButterworthHeinemann
(1984).
PHY604: Review of quantum mechanics


[Cr:4,
Lc:2,
Tt:2,
Lb:0]
Course Outline

Classical
vs.
Quantum
Mechanics,
Simple
2state
QM
system.
Hilbert
Spaces,
Operators.
Observables

Compatible
Observables,
Tensor
Product
Spaces,
Uncertainty
Relations.
Position,
Momentum
and
Translation.
Eigenvalue
Problems.

Time
Evolution
(Quantum
Dynamics).
Schroedinger,
Heisenberg
and
Interaction
Pictures;
Energytime
Uncertainty,
Interpretation
of
Wavefunction.
Ehrenfest,
Quantization,
Path
Integrals.
Quantum
Particles
in
Potential
and
EM
Fields

Gauge
Invariance,
AharanovBohm.

Angular
Momentum:
SO(3)
vs. SU(2).
Lie
Algebra
and
Representations
of
SU(2).
Spherical
Harmonics.
Addition
of
Angular
Momenta.
Tensor
Operators
and
WignerEckardt
Perturbation
Theory:
RayleighSchroedinger
(Nondegenerate
Timeindependent)
Perturbation
Theory.
Examples
in
Hydrogen
Atom.

Symmetry
groups
in
QM.
Parity.
Time
reversal.
Identical
particles

permutations.
Pauli
exclusion.
Central
field
approximation.
Hartree
equations.
Scattering:
Born
approximation.
Spherical
waves.
partial
wave
scattering.
Lowenergy
scattering,
bound
states,
resonances.
Coulomb
scattering.

Relativistic
quantum
mechanics:
Dirac
equation.
KleinGordon
equation.
Relativistic
particles
and
group
theory.
Solutions
to
Dirac:
free
particle,
relativistic
Hydrogen
atom.
Recommended Reading

L.
Schiff,
Quantum
mechanics,
03rd
edition,
McGrawHill
(1968).

J.
J.
Sakurai,
Modern
quantum
mechanics,
AddisonWesley
(1993).

C.
CohenTannoudji,
Quantum
mechanics
Vols
1
and
2,
WileyInterscience
(2006).
PHY622: Mathematical methods for physicsts III


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline
Topics are divided into three groups. First set of topics and one of the other two is to be
taught in a given instance.

Linear
Algebra:
Vector
spaces,
Inner
product,
Linear
maps,
Vector
algebra,
Operator
algebra,
Conjugation
of
operators,
Hermitian
operators,
Unitary
operators,
Projection
operators,
Functions
of
operators,
Matrices,
Similarity
transformations,
Determinant,
Trace,
Direct
sums,
Subspaces,
Invariant
subspaces,
Eigenvalues
and
eigenvectors,
Spectral
decomposition,
Polar
decomposition.

Group
Theory:
Groups,
Subgroups,
Classes
and
Invariant
subgroups,
Cosets,
Factor
groups,
Homomorphism
and
isomorphism
of
groups,
Group
representations,
Reducible
and
Irreducible
representations,
Unitary
representations,
Schur’s
Lemmas,
Lie
groups
and
Lie
algebras,
Rotation
groups
SO(2)
and
SO(3),
Special
unitary
group
SU(2),
Irreducible
representations
of
SO(2),
SO(3)
and
SU(2)
and
their
applications,
Homogeneous
Lorentz
group,
Poincare
group,
Young
diagrams.

Differential
equations:
linear
and
nonlinear
differential
equations,
nonlinear
differential
equations
relevant
in
physics.
KleinGordon;
SineGordon
equation;
KdV
equations;
soliton
solutions.
Stochastic
differential
equations,
Langevin
equation,
Fokker
Planck
equations.
Recommended Reading

Sadri
Hassani,
Mathematical
Physics,
Springer
(2013).

H.
J.
Weber
and
G.
B.
Arfken,
Essential
Mathematical
Methods
for
Physicists,
Academic
Press
(2004).

WuKi
Tung,
Group
Theory
in
Physics,
World
Scientific
(2008).

M.
Hamermesh,
Group
Theory
and
Its
Application
to
Physical
Problems,
Dover
Publications
(1989).

Howard
Georgi,
Lie
Algebras
in
Particle
Physics,
Levant
Books
(2009).

J.
V.
Jose,
and
E.
J.
Saletan,
Classical
Dynamics:
A
Contemporary
Approach,
Cambridge
University
Press
(2002).

C.
Gardiner,
Handbook
of
Stochastic
Methods
for
Physics,
Chemistry
and
the
Natural
Sciences,
Springer
(2004).
PHY631: Quantum computation and quantum information


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Introducing
quantum
mechanics.
Quantum
kinematics,
quantum
dynamics,
quantum
measurements.
(The
course
is
self
contained
and
does
not
assume
a
background
in
quantum
mechanics).
Single
qubit,
multiqubits,
gates.
Density
operators,
pure
and
mixed
states,
quantum
operations,
environmental
effect,
decoherence.
Quantum
nocloning,
quantum
teleportation.

Cryptography,
classical
cryptography,
introduction
to
quantum
cryptography.
BB84,
B92
protocols.
Introduction
to
security
proofs
for
these
protocols.

Introduction
to
quantum
algorithms.
DeutschJozsa
algorithm,
Grover’s
quantum
search
algorithm,
Simon’s
algorithm.
Shor’s
quantum
factorization
algorithm.

Errors
and
correction
for
errors.
Simple
examples
of
error
correcting
codes
in
classical
computation.
Linear
codes.
Quantum
error
correction
and
simple
examples.
Shor
code.
CSS
codes.

Quantum
correlations,
Bell’s
inequalities,
EPR
paradox.
Theory
of
quantum
entanglement.
Entanglement
of
pure
bipartite
states.
Entanglement
of
mixed
states.
Peres
partial
transpose
criterion.
NPT
and
PPT
states,
bound
entanglement,
entanglement
witnesses.

Physical
realization
of
qubit
system.
Different
implementations
of
quantum
computers.
NMR
and
ensemble
quantum
computing,
Ion
trap
implementations.
Optical
implementations.
Recommended Reading

M. A. Nielsen
and
I .L. Chuang,
Quantum
Computation
and
Quantum
Information,
Cambridge
University
Press
(2000).

J. Preskill’s
Lecture
Notes
on
Quantum
Information
http://www.theory.caltech.edu/people/preskill/ph229/
PHY632: Advanced experiments in physics


[Cr:4,
Lc:0,
Tt:0,
Lb:12]
Course Outline
This course is intended for Advanced MS (Physics Major) students with an interest in
gaining experience in an experimental physics research group. The course can
be offered every semester, with a set of instructors drawn from the available
experimental research groups. The mode of instruction will comprise a combination of
lectures, tutorials and minor research projects to be carried out in the research
lab of the concerned instructor currently the available modules are as follows
out of which depending upon the instructs at least two will be included in the
course.

NMR
Spectroscopy
Lab:
Applying
the
Fourier
transform
to
the
NMR
signal.
Digital
data
processing,
Nyquist
theorem,
Discrete
Fourier
transform,
FFT
algorithm,
window
functions
and
apodization.
Physical
basis
of
the
NMR
signal,
phase
correction,
phase
cycling.
RedfieldBloch
relaxation
theory
and
Master
equation
approach
to
identifying
relaxation
processes
in
systems
of
two
and
three
coupled
spins.
The
basic
2D
FTNMR
experiment
and
application
to
finding
the
structure
of
a
biomolecule.
Pulsed
field
gradients
and
understanding
diffusion
processes
in
polymer
chains.
Selective
pulse
rotations,
composite
pulses
and
implementation
of
an
NMR
Quantum
Computing
algorithm.

Femtosecond
Laser
Lab:
Experiments
with
cw
laser,
cavity
stability,
beam
parameters,
divergence,
diameter,
intracavity
frequency
doubling.
Experiments
with
femtosecond
laser:
measurement
of
femtosecond
laser
parameters,
pulse
duration,
autocorrelation,
spectral
width,
repetition
rate,
beam
diameter,
divergence,
application
of
fs
pulses
to
measure
speed
of
light
in
vacuum,
air
and
in
glass.
Pumpprobe
spectroscopy,
interferometric
stability,
ultrafast
phenomenon
measured
by
fs
pump
probe
setup.

Low
Temperature
Physics
Lab:
This
lab
will
focus
on
low
noise
electronics.
Projects
will
involve
integrating
different
electronic
equipments
in
one
Labview
programme.
As
an
example
varying
gate
voltage
from
a
DAQ
card
output
and
measuring
the
conductance
using
a
lockin
amplifier
(
a
mock
device
like
a
commercial
JFET
or
MOSFET
will
be
used).
Students
will
also
do
some
hands
on
Radiofrequency
electronics
like
designing
coplanar
waveguides
on
a
PCB
.
They
will
be
expected
to
understand
concepts
like
noise
figures
and
noise
temperatures,
develop
cryogenic
amplifiers
to
be
tested
at
liquid
nitrogen
temperatures.

Solid
State
Physics
Lab:
Students
will
make
new
compounds
by
mixing
up
starting
materials/chemicals.
These
could
be
superconducting,
magnetic,
or
could
show
other
interesting
properties.
Students
will
also
do
characterization
and
imaging
of
these
and
other
materials
using
a
Scanning
Electron
Microscope
(SEM).
Specifically
students
will
look
at
gold
nanoparticles
and
the
wonder
material
graphene
using
the
SEM.
Recommended Reading

M. Sayer
and
A. Mansingh,
Measurement,
Instrumentation
and
Experiment
Design
in
Physics
and
Engineering,
PrenticeHall
of
India
Pvt.Ltd
(2004).

D. M. Pozar,
Microwave
Engineering,
03rd
edition,
Wiley
(2004)

E. Fukushima
and
S .B. Roeder,
Experimental
Pulse
NMR:
A
nuts
and
bolts
approach,
Westview
Press
(1993)

R. C. Richardson
&
E. N. Smith,
Experimental
Techniques
In
Condensed
Matter,
Westview
Press
(1998).
PHY633: Mesoscopic physics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Review
of
quantum
mechanical
notation.
Basic
problems
in
QM
like
transmission
via
a
potential
well,
density
of
states
Fermi
golden
rule,
Landau
quantization
of
electrons
in
magnetic
field
and
AharonovBohm
effects.

Review
of
semiconductor
concepts
.
Overview
of
fabrication
techniques
of
mesoscopic
devices

2D
electrons
confined
to
semiconductor
heterostructures.
Quantized
Hall
phenomena
and
associated
ShubnikovdeHass
Oscillations.
Phenomenological
theory
along
Laughlin’s
gauge
invariance
arguments
,
WidomSreda
thermodynamic
formulations,
followed
by
Thouless’s
winding
number
approach.
Scaling
theory
of
localization
in
1D
and
2D.
2D
systems
showing
metallic
phases
due
to
ee
interactions.
Wigner
crystals
in
extremely
dilute
2D
electron
systems
in
high
magnetic
fields.
Other
2D
electron
systems
like
graphene,
electrons
on
helium
surfaces
and
organic
transistors.

Landauer
transmission
formalism.
Application
of
formalism
to
explain
quantized
conductance
of
devices
like
quantum
point
contacts.
Weak
localization
nd
AharonovBohm
effect
in
gold
rings
and
other
systems.
Violation
of
Kirchhoff’s
circuit
laws
for
quantum
conductors.

Overview
of
superconductors.
London
equations
.
Classic
flux
quantization
experiments
of
Doll
&
Nabauer
,
Deaver
&
Fairbank.
Josephson
effect
and
SQUIDS.
Landau
Zener
tunneling
and
Macroscopic
quantum
effects
in
SQUID
based
devices.

Nanomechanical
systems.
Applications
to
mass
sensing
filters
etc.
Dissipation
phenomena
in
nanomechanical
resonators
and
possibility
of
achieving
macroscopic
quantum
states
in
mechanical
systems.

Spintronics.
JohnsonSilsbee
experiments
,
Datta
Das
Transistors
,
Giant
magnetoresistance
and
applications
.
Recommended Reading

Y.
Murayama,
Mesoscopic
Systems,
Wiley
VCH
(2001).

S. Datta,
Electronic
Transport
in
Mesoscopic
Systems,
Cambridge
University
Press
(1997).

A.
Cleland,
Foundations
of
Nanomechanics,
Springer
(2001).

M. Ziese
and
M. J. Thornton,
Spin
Electronics
(Lecture
Notes
in
Physics),
Springer
(2001).
PHY634: NMR in physics and biology


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline
The course is intended for advanced MS and PhD students with an interest in
applications of nuclear magnetic resonance (NMR) to problems in structural biology,
medicine and physics. The course will also include tutorials and handson experience with
actual data obtained from the NMR facility.

Physical
basis
of
the
NMR
signal.
Bloch
equations
and
the
macroscopic
view.
Zeeman
splitting,
Larmor
precession,
Resonance
phenomenon,
Spin
echo.
The
NMR
spectrometer.
Basic
hardware
components
including
the
magnet,
rf
transmitter,
probe
and
receiver.
Fourier
transform
NMR.
Digitizing
the
signal
using
the
DFT.
The
FFT
algorithm.
The
rf
pulse
and
its
excitation
profile.
Data
processing
techniques
for
resolution
enhancement
and
S/N
improvement

The
chemical
shift.
The
diamagnetic
effect
and
the
paramagnetic
term.
Chemical
shift
anisotropy.
Hydrogen
bonding.
Scalar
coupling.
Investigation
of
exchange
processes.
The
Nuclear
Overhauser
effect
(NOE).
The
density
matrix
and
the
product
operator
formalism.
Rf
pulses
and
evolution.
Coherence
transfer.
Origins
of
relaxation
in
systems
of
coupled
spins.
Application
to
gaining
information
about
dynamics
in
biomolecules
over
biologically
relevant
timescales.
The
TROSY
experiment.

The
basic
2DNMR
experiment.
Extension
to
three
dimensions.
Assignment
strategies,
triple
resonance
experiments
and
structure
determination
protocols
for
proteins.

Overview
of
new
and
exciting
developments
in
NMR:
Nucleic
acids
and
macromolecular
assemblies.
Drug
design
and
discovery.
Fast
acquisition.
Metabolic
studies
by
NMR.
Residual
dipolar
couplings.
Protein
folding
by
NMR.

Pulsed
field
gradients
and
studies
of
diffusion
by
NMR.
Applications
to
the
physics
of
polymers,
nonNewtonian
fluids
and
macromolecular
crowding.

Basics
of
Magnetic
Resonance
Imaging
(MRI).
Use
of
magnetic
field
gradients
to
create
a
correspondence
between
intensity,
frequency
or
phase,
and
spatial
coordinates.
fMRI
(Functional
MRI)
and
imaging
processes
in
the
brain
Basics
of
flow
and
MR
angiography.
Recommended Reading

M.
H.
Levitt,
Spin
DynamicsBasics
of
Nuclear
Magnetic
Resonance,
02nd
edition,
Wiley
(2008).

J.
Cavanagh,
W.
J.
Fairbrother,
A.
G.
Palmer
III
and
N.
J.
Skelton,
Protein
NMR
spectroscopy,
principles
and
practice,
2nd
edition,
Academic
Press
(2006).

B. Blumich,
Essential
NMR:
For
scientists
and
engineers,
Springer
(2005).

J. Keeler,
Understanding
NMR
spectroscopy,
2nd
edition,
Wiley
(2010).

K. V. R
Chary
and
G. Govil,
NMR
in
Biological
Systems:
From
molecules
to
human,
Springer
(2008).

M. L. Lipton
and
E. Kanal,
Totally
accessible
MRI,
Springer
(2008).

D. W. McRobbie,
E. A. Moore,
M. J. Graves
and
M. R. Prince,
MRI
from
Picture
to
Proton,
2nd
edition,
Cambridge
University
Press
(2007).
PHY635: Gravitation and cosmology


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Knowledge of the content of PHY301, PHY303 and PHY310 is essential to follow
this course.
Course Outline

Review
of
special
relativity
and
Newtonian
gravity.

Equivalence
principle,
local
inertial
frames.

The
metric
tensor.
Measurements
of
lengths
and
synchronization
of
clocks.

Coordinate
transformations,
manifolds
and
tensors.

Christöffel
symbols,
geodesic
equation,
geodesic
deviation
equation
and
the
curvature
tensor.

Stressenergy
tensor,
Bianchi
identities,
Einstein’s
equation.

Maxwell’s
equations
in
curved
space
time,
stressenergy
tensor
for
the
electromagnetic
field.

Synchronous
coordinates.

Gravitational
field
of
a
point
mass,
Schwarzschild
metric
and
black
holes.
Orbits
around
a
point
mass,
precession
of
perihelion,
lensing
equation.
The
horizon
and
the
singularity
in
the
Schwarzschild
metric.

Gravitational
field
of
a
star,
interior
and
exterior
solutions,
gravitational
field
of
a
rotating
body,
Kerr
metric.

Post
Newtonian
(PN)
and
Post
Minkowski
(PM)
description
of
theories
of
gravity.
Experimental
tests
of
the
general
theory
of
relativity.

Linearized
field
equations,
gauge
freedom.
scalar,
tensor
and
vector
modes.
Gravitational
waves.

Symmetries
and
Killing
vectors.

The
cosmological
principle,
RobertsonWalker
metric,
Friedmann
equations.
Solutions
of
the
Friedmann
equations.

Cosmological
redshift,
distances
in
cosmology.
Observational
constraints
from
distance
measurement.

CosmicMicrowave
Background
Radiation
(CMBR)
in
the
standard
cosmological
model,
flatness
and
horizon
problems,
inflationary
scenarios.

Brief
overview
of
the
thermal
history
of
the
universe
and
formation
of
large
scale
structure.
Recommended Reading

L.
D.
Landau
and
E.
M.
Lifshitz,
Classical
Theory
of
Fields,
ButterworthHeinemann
(1980).

C.
W.
Misner,
K.
S.
Thorne
and
J.
A.
Wheeler,
Gravitation,
W.
H.
Freeman
(1973).

S.
Weinberg,
Gravitation
and
Cosmology,
John
Wiley
&
Sons
(1972).

T.
Padmanabhan,
Gravitation:
Foundations
and
Frontiers,
Cambridge
University
Press
(2010).

S.
Weinberg,
Cosmology,
Oxford
University
Press
(2008).

J.
B.
Hartle,
Gravity:
An
introduction
to
Einstein’s
General
Relativity,
Benjamin
Cummings
(2003).

B.
F.
Schutz,
A
first
course
in
general
relativity,
Cambridge
University
Press
(2009).

P.
J.
E.
Peebles,
Principles
of
Physical
Cosmology,
Princeton
University
Press
(1993).

T.
Padmanabhan,
Theoretical
Astrophysics:
Volume
3,
Galaxies
and
Cosmology,
Cambridge
University
Press
(2002).

S. Dodelson,
Modern
Cosmology,
Academic
Press
(2003).
PHY636: Advanced condensed matter physics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Knowledge of the content of PHY302, PHY304 and PHY402 is essential to follow
this course.
Course Outline

Introduction
and
Motivation:
Energy,
length
and
time
scales
in
solid
state;
complexity
and
emergent
behavior;
brief
review
of
key
concepts
in
quantum
mechanics
and
statistical
mechanics.

Second
quantization:
Quantum
fields
as
creation
and
annihilation
operators;
Fermi
and
Bose
statistics;
commutation
and
anticommutation
relations.

Tightbinding
models
and
their
applications:
oneband
and
multiband
models;
electronic
structure
and
crystal
lattices;
metals
and
insulators;
magnetic
materials.

Transition
metal
compounds:
spin,
charge
and
orbital
degrees
of
freedom
and
their
interplay;
manganites;
cuperates;
pnictides.

Phase
Transitions:
Examples
of
phase
transitions;
GinzburgLandau
approach;
Renormalization
group
methods.

Special
Topics
(some
of
them
will
be
as
term
papers):
Strong
coupling
expansion;
MonteCarlo
methods;
Exactdiagonalization
methods;
BCS
theory
of
superconductivity;
doubleexchange
and
Kondolattice
models;
BoseEinstein
condensation;
Graphene
and
the
quantum
Hall
effect.
Recommended Reading

M. Tinkham,
Introduction
to
Superconductivity,
Dover
Publications
(2004).

C. J. Pethick
and
H. Smith,
BoseEinstein
Condensation
in
Dilute
Gases,
Cambridge
University
Press
(2008).

G.
D.
Mahan,
Many
Particle
Physics,
Springer
(2010).

N.
Goldenfeld,
Lectures
on
Phase
Transitions
and
the
Renormalization
Group,
Westview
Press
(1992).

A.
L.
Fetter
and
J.
D.
Walecka,
Quantum
Theory
of
Many
Particle
Systems,
Dover
Publications
(2003).

P.
Fazekas,
Lecture
Notes
on
Electron
Correlation
and
Magnetism,
World
Scientific
(1999).

N.
W.
Ashcroft
and
N.
D.
Mermin,
Solid
State
Physics,
Brooks
Cole
(1976).
PHY637: Astrophysics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Knowledge of the content of PHY301, PHY303, PHY304 and PHY403 is essential
to follow this course.
Course Outline

Brief
history
of
observational
astronomy;
retrograde
motion.
Celestial
coordinate
systems,
time
keeping
and
precession.

Kepler’s
and
Newton’s
law.
Virial
Theorem
and
its
applications.
Quantisation
of
light.
Quantifying
fluxes,
magnitudes,
fluxes,
luminosity,
colour
indices.

Types
of
telescopes
and
fundamental
principles:
Refraction,
reflection,
resolution.
Types
of
aberrations.
Types
of
mounts
and
detectors.
Nyquist
theorem.

Observing
parameters
for
photometry.
Classification
of
stellar
spectra:
Boltzmann
and
Saha
equations.

Classification
and
measurement
of
physical
quantities
for
stars.
Types
of
star
clusters
and
their
properties.
Binary
systems:
classification,
properties,
observations.

Stars
on
the
main
sequence.
Nuclear
reactions
and
generation
of
energy.
Relation
between
mass,
radius
and
luminosity
of
main
sequence
stars.
Life
time
on
main
sequence,
variation
with
mass
of
stars.
Evolution
of
stars
beyond
the
main
sequence.

Interior
of
stars:
the
LaneEmden
approximation,
pressure,
opacity
and
energy
transport.
Derivation
of
physical
properties
of
stars
with
theoretical
models.
Profiles
of
spectral
lines.
Types
and
source
of
opacities.
Extinction
curves.

Stellar
remnants:
white
dwarfs,
Chandrasekhar
limit,
Neutron
stars,
Black
holes.

Acquisition
of
data
to
final
images:
steps
in
photometry
and
spectroscopy.

Statistical
properties
of
galaxies:
morphological
classification,
fundamental
parameters,
surface
brightness,
rotation
curves
and
evidence
for
the
existence
of
dark
matter.
Structure
and
dynamics
of
elliptical
galaxies.
Groups
and
Clusters
of
galaxies.
Largescale
structure
of
the
Universe:
cosmic
filaments,
environment
of
galaxies,
distance
measurement
using
TullyFisher
method.

InterGalactic
Medium
(IGM),
Quasar
absorption
systems,
Damped
Lyman
alpha
systems.

Interstellar
medium
(ISM),
Jeans
length.
phases
of
ISM,
estimation
using
pressure
equilibrium.
photoionisation
equilibrium.

Active
galactic
nuclei.
Classification
of
AGN.
Unified
theory
of
AGN.
Radio
galaxies.
Weighing
supermassive
black
holes
using
Virial
theorem.

Expansion
of
the
universe,
Hubble’s
law.
Newtonian
cosmology.
Recommended Reading

Bradley
W.
Carroll
and
Dale
A.
Ostlie,
Introduction
to
Modern
Astrophysics,
2nd
Edition,
Addison
Wesley
(2006)

Frederick
R.
Chromey,
To
measure
the
Sky:
An
introduction
to
Observational
Astronomy,
Ist
Edition,
Cambridge
University
Press
(2010)

D.
Scott
Birney,
Guillermo
Gonzalez
and
David
Oesper,
Observational
Astronomy,
2nd
Edition,
Cambridge
University
Press
(2006)
PHY638: Physics of fluids


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Knowledge of the content of PHY301, PHY303 and PHY310 is essential to follow
this course.
Course Outline

Ideal
fluids:
Conservation
of
mass
and
the
equation
of
continuity,
Euler’s
equation,
hydrostatics,
energy
and
momentum
flux,
potential
flow,
incompressible
fluids.
Waves
in
an
incompressible
fluid.

Viscous
fluids:
Equation
of
motion,
energy
dissipation
in
an
incompressible
fluid.
Reynolds
numbers.
Laminar
wake.

Turbulence:
Stability
of
flows,
instability
of
tangential
discontinuities,
transition
to
turbulence.
Description
of
turbulent
flows
using
correlation
functions.
Turbulent
flow
and
the
phenomenon
of
separation
with
examples.

Thermal
conduction
in
fluids,
heat
transfer
in
a
boundary
layer,
heating
of
a
body
in
a
moving
fluid,
convection.

Diffusion:
The
equations
of
fluid
dynamics
for
a
mixture
of
fluids,
diffusion
of
suspended
particles
in
a
fluid.

Surface
phenomena
like
capillary
waves.

Sound:
Sound
waves,
the
energy
and
momentum
of
sound
waves,
reflection
and
refraction,
propagation
of
sound
in
a
moving
medium,
absorption
of
sound.

Shocks:
Propagation
of
disturbances
in
a
moving
gas,
surfaces
of
discontinuity,
junction
conditions,
thickness
of
shock
waves.

One
dimensional
gas
flow:
flow
of
gas
in
a
pipe,
flow
of
gas
through
a
nozzle,
onedimensional
travelling
waves,
characteristics
and
Riemann
invariants.

Physics
of
strong
explosions,
SedovTaylor
solution.
Recommended Reading

L.
D.
Landau
and
E.
M.
Lifshitz,
Fluid
Mechanics:
Volume
6
(Course
of
Theoretical
Physics),
ButterworthHeinemann
(1987).

G.
K.
Batchelor,
An
Introduction
to
Fluid
Dynamics,
Cambridge
University
Press
(2000).
PHY639: Topics in biophysics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Review
of
essential
physical
principles
and
laws,
forces,
energy,
laws
of
thermodynamics;
Life
and
its
physical
basis.

The
cell
and
its
components:
membranes,
cytoskeleton,
organelles.
The
central
role
of
macromolecules:
proteins,
nucleic
acid,
carbohydrates.
Brownian
motion
and
viscosity
and
their
influence
on
particle
motion
in
the
cell.

Cell
movement,
movements
of
proteins,
cytoskeleton,
molecular
motors,
actin,
myosin,
active
and
passive
transport,
adhesion,
cell
signalling,
Brownian
motion,
viscosity,
physics
at
low
Reynolds
number.

The
Cell
Membrane:
lipid
bilayers,
Liposomes.

Structure
and
function
of
proteins,
structural
organization
within
proteins:
primary,
secondary,
tertiary,
and
quartenary
levels
of
organization,
stability
of
proteins,
protein
folding
problem,
free
energy
and
denaturation,
motions
within
proteins,
how
enzymes
work,
measurement
of
binding
and
thermodynamic
analysis.

Nucleic
acids
and
genetic
information,
DNA
double
helix,
How
structure
stores
information,
DNA
replication
process,
From
DNA
to
RNA
to
protein,
DNA
packing,
DNA
denaturation,
unzipping,
RNA
transcription.

Neurons,
action
potential,
HodgkinHuxley
analysis,
ion
channels
and
pumps,
biophysics
of
the
synapse,
Neural
networks.

Fluorescent
imaging
techniques,
electron
microscopy,
xray
crystallography,
NMR
spectroscopy,
atomic
force
microscopy,
optical
tweezers.
Recommended Reading

R. Phillips,
J. Kondev
and
J. Theriot,
Physical
biology
of
the
cell,
Taylor
&
Francis
(2008).

M. Daune,
Molecular
biophysics
structures
in
motion,
Oxford
University
Press
(1999).
PHY640: Nonequilibrium statistical mechanics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Qualitative
comparison
of
equilibrium
and
nonequilibrium
systems.
Review
of
thermodynamic
ensembles,
phase
space
density,
Liouville
equation.

Langevin
equation,
fluctuationdissipation
theorem,
velocity
autocorrelation.

Master
equations,
ChapmanKolmogorov
equation,
KramersMoyal
expansion,
Discrete
Markov
processes,
solution
of
Master
equation,
stationary
distribution,
detailed
balance,
EinsteinSmoluchowski
equation.

FokkerPlanck
equation,
OrnsteinUhlenbeck
(OU)
distribution,
the
diffusion
equation.
Diffusion
in
three
dimensions,
Diffusion
in
a
finite
region,
reflecting
and
absorbing
boundaries.
Brownian
motion,
Wiener
processes,
relationship
between
OU
and
Wiener
processes,
Survival
probability,
mean
firstpassage
time.

Diffusion
in
a
potential,
Langevin
equation
in
an
external
potential,
Kramer’s
equation,
Brownian
oscillator,
Smoluchowski
equation,
Kramer’s
escape
rate.
Diffusion
in
a
magnetic
field.

GreenKubo
formulas,
Dynamic
mobility,
power
spectral
density,
WienerKhinchin
theorem,
white
and
colored
noise.
Recommended Reading

V.
Balakrishnan,
Elements
of
Nonequilibrium
Statistical
Mechanics,
Ane
Books,
New
Delhi
(2008).

R.
Zwanzig,
Nonequilibrium
Statistical
Mechanics,
Oxford
University
Press
(2004).

N.
G.
van
Kampen,
Stochastic
Processes
in
Physics
and
Chemistry,
North
Holland
Amsterdam
(1985).

H.
Risken,
The
FokkerPlanck
Equation:
Methods
of
Solution
and
Applications,
SpringerVerlag
Berlin
(1996).
PHY641: Advanced classical mechanics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Aim:
An
advanced
course
in
classical
mechanics
that
lays
down
the
foundation
for
further
study
of
modern
physics,
from
quantum
mechanics
to
statistical
mechanics
to
nonlinear
dynamics.
Stress
will
be
on
the
more
modern
formalisms,
concepts,
and
techniques
of
classical
mechanics
that
find
applications
in
a
variety
of
fields.

Topics:

Lagrangian
Formulation
of
Mechanics;
Constraints
and
Configuration
Manifolds;
Symmetries
and
Conservation
laws

Hamiltonian
Formulation
of
Mechanics;
Hamilton’s
Equations
of
Motion
(Symplectic
Approach)

Canonical
Transformations;
ActionAngle
Variables;
Poisson
brackets
and
Invariants;
Integrable
Systems

Canonical
Perturbation
Theory

Adiabatic
Invariants;
Rapidly
Varying
Perturbations

KAM
theorem;
Nonintegrability
and
Chaos
in
Hamiltonian
Systems

Introduction
to
Continuum
Dynamics
and
Classical
Fields
(SineGordon
Equation;
KleinGordon
equation;
Solitons)

Semiclassical
Quantization
(EinsteinBrillouinKeller
Quantization;
Gutwiller
Trace
Formula)
Recommended Reading

J. V. Jose
and
E. J. Saletan,
Classical
Dynamics

A
Contemporary
Approach,
Cambridge
University
Press
(1998).

M. Tabor,
Chaos
And
Integrability
In
Nonlinear
Dynamics:
An
Introduction,
WileyInterscience
(1989).
PHY642: Nonequilibrium thermodynamics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Knowledge of the content of PHY202 and PHY304 is essential to follow this
course.
Course Outline

Review
of
equilibrium
thermodynamics:
Laws
of
thermodynamics,
Gibbs
equation,
Legendre
transforms
of
thermodynamic
potentials.
Stability
of
equilibrium
states.

Classical
Irreversible
thermodynamics
(CIT):
Generalized
forces
and
fluxes,
Local
equilibrium
hypothesis,
Onsagar
reciprocity
relations,
stationary
states,
minimum
entropy
production,
applications,
limitations
of
CIT.

Coupled
transport
phenomena:
Thermoelectric
effect,
Seebeck
effect,
diffusion
through
a
membrane.

Finitetime
thermodynamics:
Finite
time
Carnot
cycle,
Generalized
potentials,
thermodynamic
length,
criteria
for
optimal
performance.
Quantum
models
of
heat
engines.

Extended
irreversible
thermodynamics:
Heat
conduction,
Fourier
vs.
Cattaneo’s
law,
extended
entropy,
nonlocal
terms,
applications.
Recommended Reading

G. Lebon,
D. Jou
and
J. CasasVazquez,
Understanding
Nonequilibrium
Thermodynamics,
Springer
(2008).

H.
B.
Callen,
Thermodynamics
and
an
Introduction
to
Thermostatistics,
2nd
edition,
John
Wiley
and
Sons
(1985).

I.
Prigogine,
Introduction
to
Thermodynamics
of
Irreversible
Processes,
3rd
edition,
Interscience
Publishers
(1967).

S.
R.
De
Groot
and
P.
Mazur,
Nonequilibrium
Thermodynamics,
Dover
Publications,
New
York
(2011).
PHY643: Electrodynamics of continuous media


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Review
of
Maxwell’s
equations
in
free
space.
Definition
of
auxiliary
fields
in
Matter
and
Maxwell’s
equations
in
materials.

Electrostatics
of
conductors,
Brief
overview
of
thermodynamic
relations
and
Electrostatics
of
Dielectrics.

Steady
currents
in
matter,
Drude
model,
Galvanomagnetic
phenomena,
Thermoelectric
and
Thermomagnetic
Phenomena
Static
magnetic
fields,
gyromagnetic
phenomena

Superconductivity
(London’s
Phenomenological
formulation)
Quasi
static
effects
,
skin
effect
overview
of
circuit
theory

Electromagnetic
waves
in
material
media.
Kramers
Kronig
relations
for
AC
susceptibilities
Wave
guides.
Recommended Reading

L.
D.
Landau
&
E.
M.
Lifshitz
Electrodynamics
of
Continuous
media,
2nd
edition
Elsevier
(1981).

R.
Becker,
Electromagnetic
fields
&
Interactions,
Dover
Publications
(1982).

M. W. Zemansky,
Heat
&
Thermodynamics,
7th
edition,
McGraw
Hill
(1997).

N.
W.
Ashcroft
&
N.
D.
Mermin,
Solid
State
Physics,
Holden
Day
(1976).
PHY644: Foundations of quantum mechanics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Introduction
Quantum
theory
(QT)
is
empirically
a
very
successful
theory;
there
is
however
an
apparent
lack
of
understanding
of
the
theory.
This
is
mostly
due
to
the
fact
that,
unlike
the
spacetime
structure,
the
cut
between
the
ontology
and
epistemology
in
QT
is
difficult
to
resolve.
The
two
fundamental
concepts–the
nonlocal
correlations
(entanglement)
between
spacelike
separated
systems
and
the
indistinguishability
(nonorthogonality)
of
quantum
states–is
widely
believed
to
separate
QT
from
classical
theories.
In
this
course
we
take
a
foundational
approach
to
QT
from
the
outside:
i.e.,
since
classical
theories
are
completely
devoid
of
entanglement,
it
is
compared
with
various
foil
theories
that
are
also
nonlocal
and
indistinguishable
in
the
sense
of
QT,
such
that
their
special
nature
in
the
theory
can
be
quantified.
The
two
concepts
will
be
explained
in
this
course
through
the
variety
of
topics
it
has
motivated
in
the
field
of
quantum
information
and
computation,
or
vice
versa.

Mathematical
Review:
The
review
of
the
Hilbertspace
formulation
of
quantum
mechanics,
quantum
states,
quantum
dynamics,
and
measurements
qubits,
blocksphere
representation,
Pauli
algebra,
pure
versus
mixed
states,
tensorproduct,
entanglement,
purification,
VECing
an
operator,
quantum
operations,
LOCC,
unitary
versus
nonunitary
dynamics,
decoherence,
positive
versus
completely
positive
maps,
Kraus
decomposition

Correlations:
EPR
paradox,
the
realism
and
nosignaling
principle,
the
hidden
variable
theories,
the
violation
of
Belltype
inequalities
by
entangled
states
(CHSH,
Mermin,
and
Svetlichny
inequalities),
Nonlocal
PR
box,
simulating
quantum
correlations,
shared
randomness,
entanglement
and
computational
complexity

Indistinguishability:
discrimination
and
estimation
of
unknown
quantum
states,
von
Neumann
versus
POVM
measurements,
quantum
tomography,
nature
of
probabilities
in
QT,
contextuality,
Gleason’s
theorem,
KochenSpecker
theorem,
compression
of
information,
Von
Neumann
entropy,
accessible
information
and
Holevo’s
theorem,
bit
commitment,
efficient
simulation
of
Hamiltonian
dynamics
Recommended Reading

A. Peres,
Quantum
Theory:
Concepts
and
Methods,
Kluwer
Dordrecht
(1995).

J. S. Bell,
Speakable
and
Unspeakable
in
Quantum
Mechanics,
Cambridge
University
Press
(2004).

M. A.
Nielsen
and
I. L. Chuang,
Quantum
Computation
and
Quantum
Information,
Cambridge
University
Press
(2000).

J. Preskill’s
Lecture
Notes
on
Quantum
Information
http://www.theory.caltech.edu/people/preskill/ph229/

B.
Schumacher
and
M.
D.
Westmoreland,
Quantum
Processes,
Systems
and
Information,
Cambridge
University
Press
(2010).
PHY645: Topics in quantum physics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Classical
limit
of
Quantum
mechanics:
Semiclassical
quantization,
WKB.
Coherent
states
as
“best
approximants”
to
classical
behaviour.
Squeezed
states.
This
topic
will
explore
solutions
of
the
Schroedinger
equation
using
approximate
methods,
mainly
based
on
the
saddle
point
method.
Relationships
to
BohrSommerfeld
methods
and
to
the
path
integral
will
lead
to
approximate
wavefunctions,
energy
levels,
and
to
classical
mechanics.

Perturbation
theory:
time
dependent
and
independent,
Standard
material
including
degenerate
cases.
Borel
resummation,
Diagrammatics,
Fermi
golden
rule
Non
perturbative
effects.
Instantons.

Quantum
systems
in
classical
fields:
AharonovBohm,
Landau
levels
etc.
Studying
quantum
systems
coupled
to
classical
electric
and
magnetic
fields.
Phases
in
quantum
mechanics.
Hall
effect,
Hofstadter
problem.
Problems
with
Semiclassical
theory
of
radiation
(BohrRosenfeld
analysis).

Scattering
theory:
1d,
2d
and
3d.
Poles
of
the
scattering
matrix.
Analyticity
properties.
Reference:
e.g.,
Sakurai

Symmetry
in
Quantum
mechanics:
Ordinary
and
supersymmetry.
Conserved
quantum
numbers.
Degeneracy
and
splitting.
WignerEckart
theorem
Representations
of
symmetry
groups.
Galilean
invariance
in
quantum
mechanics

Matrix
Quantum
Mechanics
(and
quantum
gravity):
This
topic
will
explore
the
quantum
mechanics
of
systems
with
large
numbers
of
degrees
of
freedom.
Large
N
limit,
Nuclear
energy
levels,
ThomasFermi
model,
and
a
relation
to
quantum
gravity
are
possible
sidelights.

Quantum
Light:
Quantum
description
of
optical
fields.
classical
and
nonclassical
light.
Photon
statistics,
subPoisson
light,
squeezed
light.
Recommended Reading

J. J. Sakurai,
Modern
Quantum
Mechanics,
Addison
Wesley
(1993).

S. Coleman,
Aspects
of
symmetry:
Selected
Erice
lectures,
Cambridge
University
Press
(1988).

L. Mandel
and
E. Wolf,
Optical
Coherence
and
Quantum
Optics,
Cambridge
University
Press
(1995).
PHY646: Quantum field theory and the Standard Model


[Cr:4,
Lc:4,
Tt:0,
Lb:0]
Knowledge of the content of PHY424 is essential to follow this course.
Goal: To complete the introduction of all basic tools required for computation and
interpretation of observables in High Energy Physics.
Course Outline

Functional
methods
and
Observables:
Generating
functionals,
Vacuum
bubbles,
and
Connected
Green’s
functions,
Combinatorics
from
functional
differentiation,
Exact
propagator
and
its
spectral
decomposition,
Functional
differentiation
for
fermionic
fields,
S
matrix
and
LSZ
formula,
Feynman
rules
for
scattering
amplitudes,
Scattering
crosssection
and
Decay
rate
calculations.

QED
and
U(1)
gauge
invariance:
Photon
propagator
and
gauge
fixing,
Feynman
rules
for
QED,
QED
processes.

Lie
groups
and
Lie
algebras:
Unitary
and
orthogonal
groups
and
their
representations,
Tensor
methods,
Nonabelian
covariant
derivative
and
field
strength,
gauge
invariant
action,
Feynman
rules
for
nonabelian
theories.

Spontaneous
symmetry
breaking:
Goldstone
theorem
and
Higgs
mechanism,
Unitary
and
Rxi
gauges
and
massive
vector
propagators,

Standard
Model:
Spontaneously
broken
chiral
gauge
theory,
CKM
mixing
and
charged
Lepton
masses,
B,
L
symmetries
of
SM
masses,
Feynman
rules
for
SM,
Effective
current
current
Fermi
theory,
Meson
and
Baryon
currents,
Pion
decay
constant,
Propagator
for
unstable
particles,
FEYNCALC,
FEYNRULES
and
MADGRAPH
for
automated
tree
calculation,
Weinberg
d=5
operator
and
neutrino
masses,
Neutrino
oscillations.

Loop
diagrams
in
scalar
QFT:
Wick
rotation,
Feynman
parameters
and
dimensional
regularization,
PassarinoVeltman
functions
and
use
of
tables
thereof,
Power
counting,
BPHZ
renormalization
of
phi^{3}
+
phi^{4}
theory,
Running
mass
and
pole
mass,
anomalous
dimensions,
Running
couplings,
Renormalization
Group
and
necessity
use
of
running
couplings.
Recommended Reading

M.
E.
Peskin
and
D.
Schroeder,
Introduction
to
Quantum
Field
Thoery,
(Westview
Press),
1995.

M.
Srednicki,
Quantum
Field
Theory,
(Cambridge
university
Press),
2007.

R.
J.
Rivers,
Path
Integral
Methods
in
Quantum
Field
Thoery,
(Cambridge
university
Press),
1988.

A.
Lahiri
and
P.
B.
Pal,
A
First
Book
of
Quantum
Field
Thoery,
(Narosa),
2007.

T.
P.
Cheng
and
L.
F.
Li,
Gauge
Theory
of
Elementary
Particle
Physics,
(Oxford
University
Press),
1988.

L.
H.
Ryder,
Quantum
Field
Theory,
(Cambridge
University
Press),
1996.

T.
Goto,
Formulae
for
Supersymmetry,
MSSM
and
More,
http://research.kek.jp/people/tgoto/
PHY647: Basic atomic collisions and spectroscopy


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Summary:
The
course
will
cover
basic
theory
of
atomic
structure,
spectroscopy
and
collisions
and
related
experimental
techniques.
I
would
like
to
stress
more
on
the
experimental
techniques,
if
the
students
are
able
to
spend
some
time
in
laboratories
doing
such
work.
Possibilities
of
visits
are
to
the
Accelerator
at
Panjab
University,
Chandigarh
and
InterUniversity
Accelerator
Centre,
Delhi.
I
haven’t
explored
these
yet,
but
would
like
to.
The
feasibility
of
such
an
arrangement
will
depend
on
the
number
of
students.

Rutherford
Scattering,
Concept
of
crosssection
Quantum
Mechanical
Scattering
Theory
Information
expected
from
studying
of
IonAtom
Collisions

Experimental
Techniques
for
measuring
scattering
crosssections
Generation
of
charged
particle
beams
and
neutral
beams
Techniques
for
detecting
charged
and
neutral
particles
and
photons

Theory
of
atomic
spectra,
fine
structure.
Information
expected
from
studying
atomic
spectra.

Experimental
techniques
for
spectroscopy
Lineshape,
absoprtion,
emission
Optical
spectrographs
Methods
of
excitation.
Recommended Reading

B. H. Bransden
and
C. J. Joachain,
Physics
of
Atoms
and
Molecules,
Longman
Publishing
Group
(1982).

H. E. White,
Atomic
Spectra,
McGraw
Hill
(1934).

M. R. C. McDowell,
Introduction
to
the
theory
of
ionatom
collisions,
NorthHolland
Publishing
(1970).

J. A. R. Samson,
Techniques
of
Vacuum
Ultraviolet
Spectroscopy,
V
U
V
Associates
(1990).

J. M. Hollas,
Modern
Spectroscopy,
Wiley
(2004).

W. Demtroder,
Laser
Spectroscopy,
Springer
(2008).
PHY648: Laser fundamentals and applications


[Cr:4,
Lc:4,
Tt:0,
Lb:0]
Course Outline

Basics
of
radiationmatter
interaction:
Einstein
theory
of
absorption
and
emission
in
thermal
equilibrium,
spontaneous
and
stimulated
emission,
Einstein
coefficients.

Laser
Fundamentals:
Lasing
principle,
optical
pumping,
population
inversion,
light
amplification,
self
sustained
coherent
oscillations.

Laser
rate
equations:
Two,
three
and
four
level
systems,
Laser
cavities
&
modes,
Plane
&
spherical
resonators,
Mode
selection.

Lasers:
HeNe,
CdSe,
Argon
ion,
CO2,
Nd:YAG,
Nd:
Glass,
Semiconductor
lasers,
Dye
lasers,
Ti:sapphire
lasers.
fiber
lasers,
free
electron
lasers.

Qswitching,
Mode
locking,
Holeburning,
Pulse
compression
and
ultrashort
pulse
lasers.

Additional
topics
which
are
useful
in
this
course:
Nonlinear
processes:
Propagation
of
light
waves
in
a
nonlinear
optical
media,
anisotropic
nonlinear
medium,
Second
harmonic
generation,
Phase
matching,
Four
wave
mixing,
Stimulated
Raman
scattering,
Optical
Kerr
effect,
Pockel
effect.
Other
nonlinear
processes.
Advanced Topics
Role of lasers in quantum optics experiments, Laser spectroscopy, Lasing without
inversion, extremely narrow line width lasers. Laser cooling and trapping of atoms,
Bose Einstein condensation.
Recommended Reading

Thyagarajan
and
Ghatak,
Lasers–Fundamentals
and
Applications
2nd
Edn.
Springer

Orazio
Svelto
Principles
of
Laser
5th
Edn.
Springer.

B
B
Laud,
Lasers
&
Nonlinear
Optics,
Wiley
Eastern,
(1985)
PHY649: Advanced experiments in physics: Lasers and optics


[Cr:4,
Lc:0,
Tt:0,
Lb:12]
Course Outline
This elective course aims to provide hands on training and exposure to the
forefront of laser Physics and optical technology. The emphasis would be to
assemble few thought provoking experiments from scratch on an opticaltable.
Indulging into some openended experimentation and original thinking would be
encouraged.
One would learn nuts and bolts of various available lasers, including the Femtosecond
laser system. Coherent manipulation of light by various (bio)photonic crystal and
optomechanics of fluid interfaces by radiation pressure shall be covered among other
relevant topics.
Suggested modules

Basics
of
laser
operation
and
working

Training
session
with
femtosecond
lasers

Deformation
of
fluid
interfaces
by
radiation
pressure
of
a
laser
beam

Understanding
and
characterization
of
Photonic
crystals

Interferometric
techniques
for
thinfilm
characterizations

Laser
safety
and
radiation
hazard

Optical
spectroscopy
of
various
light
sources
Suggested reading

A.
E.
Sigman,
Lasers,
University
Science
Books,
1986.

A.
Ghatak,
Optics
McGrawHill,
2008.
PHY650: Ultra low temperature physics


[Cr:4,
Lc:2,
Tt:0,
Lb:10]
Course outline
The course will have lecture components that introduce both experimental and
theoretical ideas in low temperature physics. The remaining hours will involve
hands on experience in designing and experiments in the ultra low temperature
laboratory.
Review of laws of thermodynamics

liquefaction
of
helium
and
properties
of
liquid
helium
including
phenomena
like
superfluidity
,
second
sound,
phenomenological
two
fluid
theories.
Landau
theory
of
quasiparticles,
vortices
and
quantization
of
circulation

Properties
of
Helium
3
and
Helium3
helium
4
mixtures

Solid
state
systems
below
4.2K
(
mainly
acoustic
,
thermal
and
electronic
properties
)

Overview
of
topics
like
superconductivity
spin
glasses

Tehcniques
below
4.2K
,
Adiabatic
demagnetization
,
principles
of
helium3
helium
4
refrigeration,
nuclear
demagnetization
techniques
to
reach
temperatures
below
1mK

Electronics
and
instrumentation
below
4.2K
examples
like
discovery
of
cosmic
microwave
background
(CMB)
using
cryogenic
amplifiers

Low
temperature
thermometry
including
modern
techniques
like
coulomb
blockade
primary
thermometry

Modern
cryofree
techniques
to
reach
below
10
K
.
Recommended reading

C.
Enss
&
S.
Hunklinger,
Low
temperature
Physics,
Springer
(2005)

G.K.
White
&
P.
Meeson
Experimental
Techniques
in
low
temperature
physics
Oxford
(2002)

D.S.
Betts
An
Introduction
to
Millikelvin
Technology
Cambridge
(1989)
PHY652: Phase transition and critical phenomena


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Review
of
thermodynamics
and
equilibrium
Statistical
Mechanics.
Partition
function
for
interacting
system,
virial
expansion.
Zeros
of
the
partition
function.

Ising
model,
mean
eld
theory,
Brag
Williams
approximation.
Equivalence
of
Ising
model
to
other
models,
Spontaneous
magnetization,
Solution
of
Ising
model
using
transfer
matrix,
high
and
low
temperature
expansions
and
Monte
Carlo
simulations.

Order
parameter,
correlation
function,
critical
exponents,
scaling
hypothesis,
importance
of
dimensionality.
Landau
free
energy,
LandauGinzburg
mean
eld
theory,
Functional
integration,
Gaussian
model.

Renormalization
group
transformations,
xed
points,
real
and
momentum
space
renormalization.

Nonlinear
model,
XY
model,
Two
dimensional
solids
and
melting
(KosterlitzThouless
transition).
Recommended Reading

Kerson
Huang,
Statistical
Mechanics,
Second
Ed.
John
Wiley
Sons,
Singapore
2000.

R.
K.
Pathria,Statistical
Mechanics,
Second
Ed.
ButterworthHeineman
Oxford
1996.

N.
Goldenfeld,
Lectures
on
Phase
Transitions
and
the
Renormalization
Group,
Levant
Books,
Kolkata
2005.

J.
J.
Binney,
N.
J.
Dowrick,
A.
J.
Fisher
&
M.
E.
J.
Newman,The
theory
of
Critical
Phenomena,
Oxford
2002.

J.
M.
Yeomans,
Statistical
Mechanics
of
Phase
Transitions,
Oxford
1997.
PHY653: Physics of polymers


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline
Introduction to polymers, coarsegraining in polymers. Brownian motion and
stochastic processes, OrnsteinUhlenbeck process, FluctuationDissipation theorem,
Correlation and response functions,FokkerPlanck and Smoluchowski equation and its
application. Interacting Brownian particleshydrodynamic interactions and its
origin. Review of equilibrium statistical mechanicscanonical and microcanonical
ensembles.

Statics
of
single
chain
polymers
end
to
end
distance,
distribution
of
end
to
end
distance
in
models
of
polymer
(freely
jointed
chain,
freely
rotating
chain,
Wormlike
chain
model
and
Gaussian
chain).

Dynamics
of
single
chain
Rouse
model,
Zimm
model,
density
modes
and
dynamical
scaling.
Viscoelasticity
origin
of
viscoelasticity,
constitutive
relations,
microscopic
stress
tensor.

Statics
and
Dynamics
of
many
chain
systems:
Thermodynamics
of
mixing
Entropy
and
free
energy
of
mixing,
FloryHuggins
theory,
classi
cation
of
good
and
poor
solvents,
Gaussian
approximation
to
concentration
uctuation,
scaling
theory
statics.

Dynamics
of
the
density
modes
wavevector
dependent
relaxation
times.
scaling
theory
dynamics.

Rod
like
polymers:
rotational
and
translational
di
usion.
Dynamic
light
scattering
of
rod
like
polymers.
Onsager
theory
of
phase
transition
isotropic
and
nematic
order.

Experimental
tools
in
polymer
physics
intermediate
scattering
functions,
static
and
dynamic
structure
factors.
Recommended Reading

M.
Rubinstein
&
Ralph
H.
Colby.,
Polymer
Physics
(Chemistry),
Oxford
University
Press,
USA,
1
edition,
6
2003.

PierreGilles
de
Gennes,
Introduction
to
Polymer
Dynamics
(Lezioni
Lincee),
Cambridge
University
Press,
9
1990.

M.
Doi
&
S.
F.
Edwards.
The
Theory
of
Polymer
Dynamics
(Monographs
on
Physics),
Oxford
University
Press,
USA,
12
1986.

PierreGilles
Gennes,
Scaling
Concepts
in
Polymer
Physics.,
Cornell
University
Press,
1
edition,
11
1979.

Crispin
Gardiner,
Stochastic
Methods:
A
Handbook
for
the
Natural
and
Social
Sciences
(Springer
Series
in
Synergetics),
Springer,
softcover
reprint
of
hardcover
4th
ed.
2009
edition,
10
2010.

N.
G.
Van
Kampen,
Stochastic
Processes
in
Physics
and
Chemistry,
Third
Edition
(NorthHolland
Personal
Library),
North
Holland,
3
edition,
5
2007.
PHY654: Cosmology and galaxy formation


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Knowledge of the content of PHY635 is essential to follow this course.
Course Outline

Galaxies,
types
of
galaxies,
morphological
distribution,
large
scale
distribution
of
galaxies,
clustering
of
galaxies,
large
scale
homogeneity
and
isotropy,
A
cosmic
inventory.

Hubbles
law,
expansion
of
the
universe,
comoving
coordinates.

Cosmological
principle,
FriedmanRobertsonWalkerLemaitre
model,
Cosmological
models.
Distance
redshift
relation.
Luminosity
distance
and
angular
diameter
distance.
Measurement
of
Hubbles
constant,
age
of
the
universe,
distance
measurements
and
estimation
of
cosmological
parameters.
Accelerated
expansion.

Newtonian
limit,
nonrelativistic
perturbation
theory,
growth
of
perturbations
in
the
linear
limit.
Nonlinear
growth
of
perturbations.
NBody
simulations.

Dark
matter
halos,
universal
density
profiles.

Theory
of
mass
functions,
excursion
sets,
merger
rates
for
halos.

Formation
of
galaxies,
feedback
from
star
formation
and
evolution
of
galaxies.
Super
massive
black
holes
and
active
galactic
nuclei.
Comparison
of
models
with
observations.

Clusters
of
galaxies,
intracluster
medium,
SunyaevZeldovich
effect.

History
of
the
universe:
the
dark
ages,
formation
of
first
galaxies,
reionization,
evolution
of
the
inter
galactic
medium.
Revisiting
the
cosmic
inventory.
Recommended Reading

Large
Scale
Structure
of
the
Universe,
P.
J.
E.
Peebles,
Princeton
Series
in
Physics,
Princeton
University
Press,
1980.

Principles
of
Physical
Cosmology,
P.
J.
E.
Peebles,
Princeton
Series
in
Physics,
Princeton
Uni
versity
Press,
1993.

Structure
Formation
in
the
Universe,
T.
Padmanabhan,
Cambridge
University
Press,
1993.

Theoretical
Astrophysics,
Vol.III:
Galaxies
and
Cosmology,
T.
Padmanabhan,
Cambridge
University
Press,
2002.

Galaxy
Formation,
Malcolm
S.
Longair,
Astronomy
and
Astrophysics
Library,
Springer,
2000.

Cosmology,
S.
Weinberg,
Oxford
University
Press,
2008.

Gravitation
and
Cosmology,
S.
Weinberg,
Wiley.

Galaxy
Formation
and
Evolution,
Houjun
Mo,
Frank
van
den
Bosch
and
Simon
White,
Cambridge
University
Press,
2010.

Cosmological
Physics,
J.
A.
Peacock,
Cambridge
Astrophysics,
Cambridge
University
Press,
1998.
PHY655: Special topics in particle physics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Overview
of
Particle
Physics,
including
major
historical
and
latest
developments.

Introduction
to
Relativistic
Quantum
Mechanics
and
Quantum
Field
Theory.

Relativistic
Kinematics
and
Phase
Space:
Introduction
to
relativistic
kinematics,
particle
reactions,
Lorentz
invariant
phase
space,
twobody
and
three
body
phase
space
etc.

Invariance
principles
and
Conservation
Laws:
Invariance
in
classical
mechanics
and
in
quantum
mechanics,
parity,
charge
conjugation,
time
reversal
invariance,
CPT
theorem,
O(3),
SU(2),
SU(3),
quark
model
etc.

Abelian
and
NonAbelian
gauge
transformations:
Construction
of
lAbelian
and
NonAbelian
gauge
invariant
lagrangians.
Spontaneous
symmetry
breaking.
Spontaneous
symmetry
breaking
of
a
gauge
theory.

Standard
Model
of
Particle
Physics:
formulation
of
VA
theory
of
weak
interactions.
Electroweak
unification.SU(3)X
SU(2)X
U(1)
gauge
theory
etc.

Beyond
the
standard
model:
Flavor
mixings,
mass
matrices.
CKM
and
PMNS
matrices.
CP
violation
etc.
Grand
Unified
theories.
Recommended Reading

An
introduction
to
High
Energy
Physics,
D.
H.
Perkins,
Cambridge
Press
4th
ed.2000.

Introduction
to
Quarks
and
Partrons,
F.
E.
Close,
Academic
Press,
London,
1979.

Gauge
Theories
of
Weak,
Strong
and
Electromagnetic
Interactions,
C.
Quigg,
AddisonWesley,
1994.

First
book
of
Quantum
Field
Theory,
A.
Lahiri
and
P.
Pal,
Narosa,
New
Delhi.
2nd
ed.
2007.
PHY656: Quantum principles and quantum optics


[Cr:3,
Lc:3,
Tt:0,
Lb:0]
Course Outline

Introduction
to
fundamental
principles
of
quantum
mechanics,
quantum
superposition,
quantum
entanglement,
EPR
paradox.
Quantization
of
electromagnetic
field,
concept
of
photon,
vacuum
field,
zero
point
energy,
Casimir
effect,
coherent
states
of
light,
squeezed
states,
phase
space
representation
of
quantum
states
of
light,
classical
analogy
of
a
coherent
state.

Beam
splitter
quantum
mechanics,
first
and
second
order
interference,
MandelOu
effect,
HanburyBrownTwiss
(HBT)
effect,
HBT
effect
for
classical
and
quantum
light,
photIntroduction
to
fundamental
principles
of
quantum
mechanics,
quantum
superposition,
quantum
entanglement,
EPR
paradox.
Quantization
of
electromagnetic
field,
concept
of
photon,
vacuum
field,
zero
point
energy,
Casimir
effect,
coherent
states
of
light,
squeezed
states,
phase
space
representation
of
quantum
states
of
light,
classical
analogy
of
a
coherent
state.
Beam
splitter
quantum
mechanics,
first
and
second
order
interference,
MandelOu
effect,
HanburyBrownTwiss
(HBT)
effect,
HBT
effect
for
classical
and
quantum
light,
photon
bunching
and
antibunching,
higher
order
coherence.
Single
photon
interference
experiments,
typeI
and
type
II
down
conversion,
generation
of
entangledphotons,
polarization
entangled
photons,
experiments
based
on
entangled
photons,
quantum
erasure,
wheeler
s
delayed
choice
thought
experiment,
delayed
choice
quantum
erasure.
Atomlight
interaction,
semiclassical
model,
population
oscillations,
quantum
model
of
atomphotoninteraction,
collapse
and
revival
of
population,
dressed
state
picture
of
atomlight
interaction,
atomphoton
entanglement.
Introduction
to
laser
cooling,
optical
molasses,
magneto
optical
trap,
sisyphus
cooling,
trapping
ofneutral
atoms,
evaporative
cooling,
Bose
Einstein
condensation.
on
bunching
and
antibunching,
higher
order
coherence.

Single
photon
interference
experiments,
typeI
and
type
II
down
conversion,
generation
of
entangledphotons,
polarization
entangled
photons,
experiments
based
on
entangled
photons,
quantum
erasure,

wheeler
s
delayed
choice
thought
experiment,
delayed
choice
quantum
erasure.

Atomlight
interaction,
semiclassical
model,
population
oscillations,
quantum
model
of
atomphotoninteraction,
collapse
and
revival
of
population,
dressed
state
picture
of
atomlight
interaction,
atomphoton
entanglement.

Introduction
to
laser
cooling,
optical
molasses,
magneto
optical
trap,
sisyphus
cooling,
trapping
ofneutral
atoms,
evaporative
cooling,
Bose
Einstein
condensation.
Recommended Reading

J.
J.
Sakurai,
Modern
Quantum
Mechanics,
Pearson
Education,
Inc.

C.
Gerry,
P.
Knight,Introductory
Quantum
Optics,
Cambridge
University
Press.

M.
O.
Scully
&
M.
S.
Zubairy,
Quantum
Optics,
Cambridge
University
Press.

D.
Bouwmeester,
A.
Ekert
&
A.
Zeilinger
(Eds),
The
Physics
of
Quantum
Information
PHY657: Radiofrequency and microwave circuits


[Cr:4,
Lc:3,
Tt:0,
Lb:3]
Course Outline

This
course
will
emphasize
importance
of
radiofrequency
and
microwave
circuits
in
modern
physical
experiments
ranging
from
applications
like
fast
circuits
in
quantum
computing
or
measuring
the
cosmic
microwave
background.

Review
of
Maxwells
equations
and
basic
electrodynamics,
lumped
versus
distributed
circuit
elements
Basics
of
transmission
lines
Wave
guides,
analysis
of
microwave
networks
using
Smatrix
parameters,
smith
chart,
impedance
matching
tuning
,
passive
components
like
attenuators,
directional
couplers
,
magicTee,
phase
shifters
bias
tee,
microwave
resonators
and
planar
circuits
like
microstrips,
coplanar
waveguides.
Active
components
like
low
noise
amplifiers
and
basics
of
microwave
ICs.
Mixers
,
low
noise
amplifiers
,
basics
of
microwave
synthesizers
.

Additional
topics
:
Analogy
between
theory
of
transmission
lines
and
simple
tunneling
in
quantum
mechanics,
applications
to
physical
systems.
Microwave
instruments
like
radars.
Basics
of
test
equipment
like
network
analyzer,
RF
lockin
amplifier
.
Detailed
study
of
applications
of
Microwave
or
RF
circuits
in
selected
modern
physics
experiments
e.g.
cyclotron
resonance
of
carriers
in
semiconductors,
Nuclear
magnetic
resonance,
radio
astronomy,
rotational
spectra
of
molecules
using
microwave
spectroscopy
etc.

Laboratory
work
involves
designing,
construction
and
testing
of
few
components.
Recommended Reading

R.
E.
Collin,
Foundations
of
Microwave
Engineering,
2nd
Edition
Wiley
(2001).

D.
M.
Pozar,
Microwave
Engineering,
4th
Edition
,
Wiley
(2011).

F.
E.
Terman,
Electronic
&
Radio
Engineering,
McGraw
Hill
(1955).

J.
A.
Stratton,
Electromagnetic
Theory,
Mc
Graw
Hill
(1941).

Feynman
et.al,
Feynman
Lectures
Volume
II,
Addison
Wesley
(1964).

L.
Brilloin,
Wave
propagation
in
periodic
structures,
McGraw
Hill
(1946).

R.
Teppati
et.al,
Modern
RF
and
Microwave
Measurement
Techniques,
(The
Cambridge
RF
and
Microwave
Engineering
Series),
Cambridge
University
Press
(2013).
PHY658: Advanced QFT methods and special topics in high energy physics


[Cr:4,
Lc:4,
Tt:0,
Lb:0]
Knowledge of the content of PHY424 and PHY646 is essential to follow this
course.
Goal: To cover advanced field theoretic methods and a selection of special topics in
subareas of Theoretical High Energy Physics.
Course Outline

Renormalization
of
gauge
theories.
Power
counting
for
spinors
and
vectors.
Renormalization
of
Yukawa
theory
and
QED.
Current
conservation
and
Ward
identities.

Anomalies.
ABJ
anomalies
and
gauge
theory
consistency.
Accidental
and
approximate
symmetries
of
the
Standard
Model.
Chiral
symmetry
breaking
and
properties
of
pions
and
kaons.

Path
Integrals
and
Functional
Methods.
SchwingerDyson
equations.
1PI
and
Wilson
effective
actions.
Effective
potential.
FaddeevPopov
quantization
of
YangMills
theories.
Ghosts.
BRST
symmetry.
Renormalization
of
YangMills
Higgs.
Asymptotic
freedom
and
confinement.
Anomalies
and
functional
measure.
WessZuminoWitten
theory.
Recommended Reading

M.
Peskin
and
D.
Schroeder,
Introduction
to
Quantum
Field
Theory,
(Westview
Press),
1995.

M.
Srednicki,
Quantum
Field
Theory,
(Cambridge
University
Press),
2007.

R.
J.
Rivers,
Path
Integral
Methods
in
Quantum
Field
Theory,
(Cambridge
University
Press),
1987.

S.
Weinberg,
Quantum
Theory
of
Fields,
Volume
1,2,3
(Cambridge
University
Press),
1996.

T.
P.
Cheng
and
L.
F.
Li,
Gauge
Theory
of
Elementary
Particle
Physics,
(Oxford
University
Press),
1988.

L.
H.
Ryder,
Quantum
Field
Theory,
(Cambridge
University
Press),
1996.

T.
Goto,
Formulae
for
Supersymmetry,
MSSM
and
more,
http://research.kek.jp/people/tgoto/.
Special Topics 1: GUTs and Supersymmetry

Beyond
the
Standard
Model,
Seesaw
mechanism,
Models
for
neutrino
masses,
LeftRight
Symmetric
Model,
PatiSalam
Model.
SU(5),
SO(10)
Grand
Unification,
Fermion
masses
in
GUTs.

Supersymmetry:
Four
and
two
component
notation,
Supersymmetry
algebras,
Supermultiplets
and
superfields.
Gaugeinvariant
actions
for
chiral
superfields.
Supersymmetric
gauge
theories.
Broken
supersymmetry
and
Witten
index.
Spontaneous
supersymmetry
breaking
at
tree
level.
Supergravity
basics,
Gravitymediated
supersymmetry
breaking.
Supersymmetric
LR
models
and
GUTs.
Recommended Reading

J.
Wess
and
J.
Bagger:
Superymmetry
and
Supergravity
(Princeton
University
Press),
1992.

R.
N.
Mohapatra,
Unification
and
Supersymmetry,
(Springer),
2003.

S.
P.
Martin,
A
Supersymmetry
Primer
Perspectives
on
Supersymmetry,
pp
198,
(World
Scientific),
1998,
https://arxiv.org/abs/hepph/9709356
Special Topics 2: Lattice field theory and Nonperturbative aspects of field
theory

Lattice
Field
Theory:
Scalar
fields
on
the
lattice,
Markov
Chain
Monte
Carlo,
Metropolis
algorithm,
Statistical
and
systematic
errors,
Abelian
and
nonabelian
gauge
theories,
Gaugeinvariant
observables,
Scaling
and
continuum
limit,
NielsenNinomiya
theorem,
Fermions
on
the
lattice,
Lattice
Quantum
Chromodynamics,
Algorithms
for
fermions,
Finite
density
and
the
sign
problem,
Lattice
supersymmetry,
LargeN
gauge
theories.

Extended
Field
Configurations:
Topology
in
field
theory,
Topological
solitons
and
instantons,
‘t
HooftPolyakov
monopole,
Instantons
in
YangMills
theories,
U(1)
problem,
B,
L
violation
by
EW
instantons,
Theta
angle
and
strong
CP
problem,
Fluctuations
around
extended
field
configurations,
Vacuum
decay.
Recommended Reading

C.
Gattringer
and
C.
B.
Lang,
Quantum
Chromodynamics
on
the
Lattice:
An
Introductory
Presentation,
(Springer),
2010.

T.
Degrand
and
C.
DeTar,
Lattice
Methods
for
Quantum
Chromodynamics,
(World
Scientific),
2006.

H.
J.
Rothe,
Lattice
Gauge
Theories:
An
Introduction,
(World
Scientific),
2005.
Special Topics 3: Perturbative QCD and Collider Physics

Deep
inelastic
scattering
of
Leptons
and
Hadrons.
Parton
model
and
Parton
distribution
functions.
Bjorken
scaling.
Sum
rules.
Scaling
violation.
Factorization
and
Hard
processes.
Elementary
processes
in
QCD.
Renormalization
schemes,
Renormalization
of
composite
operators,
Operator
Product
Expansion.
Infrared
divergences,
KLN
theorem
and
IR
safe
observables,
Resummation,
Parton
shower
and
MonteCarlo
event
generators,
Elements
of
nexttoleading
order
QCD
corrections.
Recommended Reading

F.
Halzen
and
A.
D.
Martin,
Quarks
&
Leptons:
An
Introductory
Course
in
Modern
Particle
Physics,
(Wiley
India),
2008.

M.
E.
Peskin
and
D.
V.
Schroeder,
An
Introduction
to
Quantum
Field
Theory,
(Westview
Press),
1995.

R.
K.
Ellis,
B.
R.
Webber,
W.
J.
Stirling,
QCD
and
Collider
Physics,
(Cambridge
University
Press),
2003.

R.
D.
Field,
Applications
of
Perturbative
QCD,
(Basic
Books),
1989.

T.
Muta,
Foundations
of
Quantum
Chromodynamics:
An
Introduction
to
Perturbative
Methods
in
Gauge
Theories,
(World
Scientific),
2009.
PHY660: Nonlinear optics


[Cr:4,
Lc:4,
Tt:0,
Lb:0]
Course Outline

Introduction
to
anisotropic
media,
double
refraction,
wave
propagation
in
anisotropic
medium,
applications
of
index
ellipsoid,
energy
and
momentum
of
light
field
in
anisotropic
media,
wave
plates,
physics
of
polarization
controlling
devices,
electrooptic
modulators.

Concepts
of
nonlinear
phenomena,
nonlinear
electric
polarizability,
second
order
nonlinear
processes;
second
harmonic
generation,
conceptual
description
of
phase
matching,
parametric
up
and
down
conversion,
parametric
oscillators
and
amplifiers,
entangled
photon
generation.

Third
order
nonlinear
processes;
third
harmonic
generation,
optical
Kerr
effect,
self
focusing,
self
phase
modulation,
supercontinuum
generation,
cross
phase
modulation,
four
wave
mixing,
optical
phase
conjugation
and
its
applications.

Nonlinear
optical
effects
in
optical
waveguides
and
optical
fibers,
applications
of
nonlinear
optics
in
quantum
optics
experiments,
nonlinear
effects
in
BoseEinstein
condensation,
higher
order
nonlinear
effects.
Recommended Reading

The
Principles
of
Nonlinear
Optics,
Y.
R.
Shen,
John
Wiley
and
Sons
Inc
(2003).

Nonlinear
Optics,
Robert
Boyd,
Elsevier
Inc
(2008).

Nonlinear
Fiber
Optics,
G.
P.
Agrawal,
Elsevier
Inc
(2013).
PHY661: Selected topics in classical and quantum mechanics


[Cr:4,
Lc:3,
Tt:0,
Lb:0]
Course Outline

Group
theory
and
symmetry
in
physics.

Symplectic
groups
and
their
uses
in
physics,
uncertainty
relations.

Geometric
Phases
in
physics.

Classical
theory
of
constrained
systems.

Quantum
Theory
of
Angular
Momentum.

Theory
of
Wigner
distributions.

The
Wigner
theory
of
UIRs
of
the
Poincare
group.

Dissipative
quantum
mechanics.
Recommended Reading

Lectures
on
Advanced
Mathematical
Methods
for
Physicists,
Sunil
Mukhi
and
N.
Mukunda,
World
Scientific
(2010).

Symplectic
Techniques
in
Physics,
V.
Guillemin
and
S.
Sternberg,
Cambridge
University
Press
(1990).

Angular
Momentum
in
Quantum
Mechanics,
A.
R.
Edmonds,
Princeton
University
Press
(1996).

Decoherence
and
the
QuantumtoClassical
Transition,
M.
A.
Schlosshauer,
Springer
(2008).

Geometric
Phases
in
Physics,
Advanced
Series
in
Mathematical
Physics
Volume
5,
Edited
by
F.
Wilczek
and
A.
Shapere,
World
Scientific
(1989).

Constrained
Dynamics:
With
Applications
to
YangMills
Theory,
General
Relativity,
Classical
Spin,
Dual
String
Model:
Lecture
Notes
in
Physics,
Kurt
Sundermeyer,
SpringerVerlag
(1982).

Distribution
Functions
in
Physics:
Fundamentals,
M.
Hillery,
R.
F.
OConnell,
M.
O.
Scully
and
E.
P.
Wigner,
Physics
Reports,
106,
pp121167
(1984).
PHY662: Statistical physics of fields


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Collective
Behavior,
from
particles
to
fields
:
Introduction,
Phonons
&
elasticity,
Phase
transitions,
Critical
Behavior.

Statistical
Fields
:
Introduction,
The
LandauGinzburg
Hamiltonian,
Saddle
point
approximation
and
mean
field
theory,
Continuous
symmetry
breaking
and
Goldstone
modes,
Discrete
symmetry
breaking
and
domain
walls.

Fluctuations
:
Scattering
and
fluctuations,
Correlation
functions
and
susceptibilities,
Lower
critical
dimension,
Comparison
to
experiments,
Gaussian
integrals,
Fluctuation
corrections
to
the
saddle
point,
The
Ginzburg
criterion.

The
scaling
hypothesis
:
The
homogeneity
assumption,
Divergence
of
correlation
length,
Critical
correlation
functions
and
self
similarity,
The
renormalization
group
(conceptual),
The
renormalization
group
(formal),
The
Guassian
model
(direct
solution),
The
Gaussian
model
(renormalization
group).

Perturbative
renormalization
group
:
Expectation
values
in
the
Gaussian
model,
Expectation
values
in
perturbation
theory,
Diagrammatic
representation
of
perturbation
theory,
Susceptibility,
Perturbative
RG
(first
order),
Perturbative
RG
(second
order),
The
epsilon
expansion,
Irrelevance
of
other
interactions,
Comments
on
the
epsilon
expansion.

Lattice
systems
:
Models
and
methods,
Transfer
matrices,
Position
space
RG
in
one
dimension,
The
NiemeijervanLeeuwen
cumulant
approximation,
The
MigdalKadanoff
bond
moving
approximation,
Monte
Carlo
simulations.

Series
expansions
:
Low
temperature
expansions,
High
temperature
expansions,
Exact
solution
of
the
one
dimensional
Ising
model,
Self
duality
in
the
twodimensional
Ising
model,
Dual
of
the
three
dimensional
Ising
model,
Summing
over
phantom
loops,
Exact
free
energy
of
the
square
lattice
Ising
model,
Critical
behavior
of
the
twodimensional
Ising
model.

Beyond
spin
waves
:
The
nonlinear
sigma
model,
Topological
defects
in
the
XY
model,
Renormalization
group
for
the
Coulomb
gas,
Twodimensional
solids,
Twodimensional
melting.

Dissipative
dynamics
:
Brownian
motion
of
a
particle,
Equilibrium
dynamics
of
a
field,
Dynamics
of
a
conserved
field,
Generic
scale
invariance
in
equilibrium
systems,
Nonequilibrium
dynamics
of
open
systems,
Dynamics
of
a
growing
surface.
Recommended Reading

Mehran
Kardar,Statistical
Physics
of
Fields.

P.
M.
Chaikin
&
T.
C.
Lubensky,
Principles
of
condensed
matter
physics.
PHY663: Relativistic cosmology and the early universe


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Knowledge of the content of PHY635 is essential to follow this course.
Course Outline

Expansion
of
the
Universe,
FriedmanRobertsonWalkerLemaitre
model,
Geodesics
and
Distance,
geodesic
deviation,
Standard
candles
and
Standard
Rulers.

Standard
cosmological
model:
radiation
dominated
era,
matter
domination,
dark
energy
and
accelerated
expansion.
Horizon
problem,
flatness
problem.
Inflationary
paradigm.

Thermal
history
of
the
universe,
primordial
nucleosynthesis,
decoupling
of
neutrinos,
weakly
interact
ing
massive
particles,
electronpositron
annihilation,
matter
radiation
decoupling,
last
scattering
surface,
cosmic
microwave
background
radiation.

Scalar
fields
in
an
expanding
universe.
Generation
of
perturbations
in
inflation,
Tensor
and
Scalar
per
turbations,
Reheating.

Perturbations
in
an
expanding
universe.
relativistic
perturbation
theory,
growth
of
perturbations
in
dif
ferent
scenarios.
Fluctuations
in
the
cosmic
microwave
background
radiation.
Transfer
Functions,
Baryon
Acoustic
oscillations,

SachsWolfe
and
Integrated
Sachs
Wolfe
effect,
Silk
damping,
The
observed
fluctuations
in
the
cosmic
microwave
background
radiation
and
its
relation
with
Cosmological
Parameters,
Observational
constraints.

Late
time
perturbations,
geometric
effects,
redshift
space
distortions.
Recommended Reading

T.
Padmanabhan,
Theoretical
Astrophysics,
Vol.III:
Galaxies
and
Cosmology,
Cambridge
University
Press,
2002.

S.
Weinberg,
Cosmology,
Oxford
University
Press,
2008.

Ruth
Durrer,
The
cosmic
microwave
background,
Cambridge
University
Press,
2008.

Scott
Dodelson,
Modern
Cosmology,Elsevier,
2005.
PHY664: Quantum thermodynamics


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Knowledge of the content of PHY202, PHY302 and PHY304 is essential to follow
this course.
Course Outline

Review
of
Thermodynamics:
laws
of
thermodynamics,
thermodynamic
potentials,
work
extraction
processes,
entropy
and
information,
Maxwell’s
demon,
Landauer
principle.

Review
of
quantum
mechanics:
density
matrix
formalism,
composite
quantum
systems,
reduced
density
matrix,
entanglement,
purity,
quantum
entropy,
relative
entropy,
quantum
measurements.

Quantum
thermodynamic
machines:
heat
cycles,
quantum
thermodynamic
processes,
quantum
adiabatic
theorem,
thermal
efficiency,
effect
of
interacting
working
medium,
quantum
friction,
quantum
Maxwell’s
demon.

Time
evolution.
Liouvillevon
Neumann
equation,
Heisenberg
and
interaction
picture,
Markovian
quantum
master
equation,
Lindblad
operators,
weak
coupling
limit,
relaxation
to
equilibrium,
decay
of
twolevel
system,
coherence
enhanced
efficiency
of
quantum
heat
engine.
Recommended Reading

J.
Gemmer,
M.
Michel,
G.
Mahler,
Quantum
Thermodynamics:
Emergence
of
Thermodynamic
Behavior
Within
Composite
Quantum
Systems,
Lecture
Notes
in
Physics,
Springer
(2009).

G.
Mahler,
Quantum
Thermodynamic
Processes:
Energy
and
Information
Flow
at
the
Nanoscale,
Pan
Stanford
(2014).

H.
P.
Breuer
and
F.
Petruccine,
Theory
of
Open
Quantum
Systems,
Clarendon
Press,
Oxford
(2002).
PHY665: Quantum phases of matter and phase transitions


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Introduction
and
Motivation:
Brief
review
of
key
concepts
in
quantum
mechanics
and
statistical
mechanics.

Phase
Transitions:
Concept
of
phase
and
phase
diagrams,
examples
of
phase
transitions,
statistical
mechanics
and
phase
transitions,
Landau
theory
of
phase
transitions,
order
parameter,
relation
to
statistical
mechanics,
Superconducting
phase
transition.

Theory
of
superconductors:
Electrodynamics
of
superconductors,
GinzburgLandau
theory,
BCS
theory,
Abrikosovs
theory
of
type
II
superconductors,
Andersons
theory
of
disordered
superconductors,
Unconventional
supercondcutors,
heavy
Fermions,
Order
parameter
symmetry,
Josephson
effect
and
SQUID,
Superconducting
qubits.

Topological
phases
of
matter
and
topological
phase
transitions:
Quantum
Hall
effect
and
the
emergence
of
topological
invariants,
Topological
band
theory,
Model
Hamiltonians,
Topological
properties
and
protections,
Characterizing
topological
materials,
Topological
states
of
quantum
matter,
Topological
insulators,
Topological
crystalline
insulators,
Topological
superconductors,
Weyl
and
3D
Dirac
semimetals,
Topological
phase
transitions.
Recommended Reading

N.
W.
Ashcroft
and
N.
D.
Mermin,
Solid
State
Physics,
Brooks
Cole
(1976).

L.
D.
Landau;
E.
M.
Lifshitz,
Statistical
Physics,
ButterworthHeinemann,
1996.

M.
Tinkham,
Introduction
to
superconductivity,
Dover
Publications,
2004.

J.
Hajdu,
Introduction
to
the
Theory
of
the
Integer
Quantum
Hall
Effect,
(1994).

A.
Bansil,
Hsin
Lin,
and
Tanmoy
Das,
Topological
Band
Theory,
Rev.
Mod.
Phys.
88,
021004
(2016).

M.
Z.
Hasan
and
C.
L.
Kane,
Topological
Insulators,
Rev.
Mod.
Phys.
82,
3045
(2010).
PHY666: Open quantum systems


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Knowledge of the content of PHY302 and PHY403 is essential to follow this
course.
Course Outline

Quantum
probability:
Pure
states
and
statistical
mixture
of
quantum
states,
density
matrix
formalism,
composite
quantum
systems,
quantum
entropy
and
quantum
measurements.

Dynamical
equation
for
open
quantum
systems:
Quantum
dynam
ical
semigroups,
Markovian
quantum
master
equation,
microscopic
deriva
tion
of
quantum
master
equation,
weakcoupling
limit.

Decoherence:
The
decay
rates
of
an
open
system
in
quantum
Brownian
motion
and
damped
harmonic
oscilator.

Optical
quantum
master
equation:
Matter
in
quantized
radiation
fields,
decay
of
twolevel
system
in
thermal
and
squeezed
thermal
bath,
Resonance
fluorescence,
damped
harmonic
oscillator
and
CaldeiraLeggett
model.

NonMarkovian
quantum
processes:
NakajimaZwanzig
projection
operator
technique,
timeconvolutionless
projection
operator
method,
ex
act
solution
of
the
spontaneous
decay
of
a
twolevel
system,
JaynesCummings
model
of
resonance.

Stochastic
approach
for
open
quantum
systems:
Stochastic
Schrdinger
equation,
homodyne
photodetection,
hetrodyne
photodetection,
and
quan
tum
trajectory
approach.
Additional Topics

Markov
Chain
Mixing,
Random
Walks
on
Graphs.
Recommended Reading

H.
P.
Breuer
and
F.
Petruccione,
The
theory
of
open
quantum
systems,
1st
edition,
Oxford
University
Press
(2003).

U.
Weiss,
Quantum
Dissipative
Systems,
3rd
edition,
World
Scientific
(2008).

H.
Carmichael,An
Open
System
Approach
to
Quantum
Optics,
Springer
Verlag
(1991).

H.
Carmichael,
Statistical
Methods
in
Quantum
Optics
1:
Master
equa
tions
and
FokkerPlanck
Equations,
Springer
(2008).

H.
Carmichael,
Statistical
Methods
in
Quantum
Optics
2:
NonClassical
Fields,
Springer
(2008).

R.
P.
Feynman
and
F.
L.
Vernon
Jr.,
The
Theory
of
a
General
Quantum
System
Interacting
with
a
Linear
Dissipative
System,
Annals
of
Physics
281,
547607
(1963).
PHY667: Quantum magnetism


[Cr:4,
Lc:3,
Tt:1,
Lb:0]
Course Outline

Introduction:
Basic
magnetic
properties,
units
in
magnetism,
magnetic
moments
and
angular
momentum,
Bohr
magneton,
precession,
quantum
mechanics
of
the
spin.

Isolated
Magnetic
moments:
Magnetization
and
magnetic
susceptibility,
paramagnetism
and
diamagnetism,
Brillouin
function,
VanVleck
Paramagnetism,
Hunds
rules
for
the
ground
state
of
ions,
adiabatic
demagnetization.

Magnetic
moments
in
solids:
Crystalline
electric
fields,
splitting
of
orbital
degeneracy,
orbital
angular
momentum
quenching,
JahnTeller
distortion.

Interactions
between
Magnetic
moments:
Dipolar
interactions,
exchange
interactions,
origin
of
exchange,
superexchange
and
double
exchange
interactions,
RKKY
interaction.

Magnetic
ordering:
Ferro,
Ferri,
and
antiferromagnetic
ordering,
Weiss
molecular
field
models
of
magnetic
ordering,
spin
glasses,
excitations
of
the
ordered
states,
magnons,
spinwaves.

Measuring
Magnetism:

Bulk
techniques

Magnetometers,
vibrating
sample
magnetometer
(VSM),
SQUID
based
magnetometers.

Microscopic
techniques

neutron
scattering,
Nuclear
Magnetic
Resonance
(NMR),
Electron
Spin
Resonance
(ESR),
and
muon
spin
rotation
(muSR).
 Special Topics: Hubbard model, Mott insulators, Magnetism in lowdimensional
and geometrically frustrated systems, BEC of Magnons, quantum spin
liquids.
Recommended Reading

J.
Crangle
and
E.
Arnold,
Solid
State
Magnetism,(1991).

S.
Blundell,
Magnetism
in
Condensed
Matter,
(Oxford
University
Press
2005).

P.
Mohn,
Magnetism
in
the
Solid
State,
(Springer,
2005).

Ashcroft
and
Mermin,
Solid
State
Physics.
PHY668: Soft condensed matter


[Cr:4,
Lc:3,
Tt:0,
Lb:0]
Course Outline

Forces,
energies
and
timescales
in
condensed
matter
.
What
is
soft
matter
?
Basic
phenomenology
of
soft
condensed
matter
systems:
Colloids,
polymers,
membranes,
liquid
crystals.
Viscous,
elastic
and
viscoelastic
behaviour.

Order
Parameter,
Phases
and
Phase
transitions.
Symmetry,
order
parameter
and
models.
Meanfield
theory
and
phase
diagrams.
Landau
theory.
Liquidgas
transition,
solidliquid
transition,
Ramakrishnan
and
Yussouff
density
functional
theory.

Colloidal
Systems.
Single
colloidal
particle
in
a
liquid
Stokes
law
and
Brownian
motion,
Forces
between
colloidal
particles.
Depletion
interactions.
Stability
and
phase
behavior
of
colloids.

Polymers.
Model
systems,
chain
statistics,
polymers
in
solutions
and
in
melts,
flexibility
and
semiflexibility,
distribution
functions,
selfavoidance,
rubber
elasticity,
viscoelasticity,
reptation.

Surfaces,
Interfaces
and
Membranes.
Interfacial
tension.
Fluctuation
of
Interfaces.
Wetting.
Fluid
vs.
solid
membranes,
energy
and
elasticity,
surface
tension.

Liquid
Crystals.
Liquid
crystal
phases.
NematicIsotropic
transition.
Distortions
and
topological
defects.
Frederiks
transition.
Polymer
liquid
crystals.

Soft
Biological
Materials.
Composition
of
cell.
Cellular
cytoskeleton.
Statistical
view
of
dynamics
inside
a
cell
:
Active
vs.
Passive
transport.
Introduction
to
soft
active
matter.
Recommended Reading

R.
A.
L.
Jones,
Soft
condensed
matter,
Oxford
University
Press
2002.

I.
W.
Hamley,
Introduction
to
soft
matter,
Wiley,
New
York
2007.

M.
Doi,
Soft
matter
physics,
Oxford
University
Press
2013.

P.
M.
Chaikin
&
T.
C.
Lubensky,
Principles
of
condensed
matter
physics,
Cambridge
University
Press
1995.

T.
A.
Witten,
Structured
fluids
–
polymers,
colloids,
surfactants,
Oxford
University
Press
2004.

P.
Nelson,
Biological
physics,
Freeman,
New
York
2004.

L.S.
Hirst,
Fundamentals
of
soft
matter
science,
CRC
Press,
London
2013.

J.
V.
Selinger,
Introduction
to
the
theory
of
soft
matter,
Springer,
New
York
2016.

M.
Kleman
&
O.
D.
Lavrentovich,Soft
matter
physics,
Springer,
New
York
2003.

S.
Safran,
Statistical
Thermodynamics
Of
Surfaces,
Interfaces,
And
Membranes,
(Frontiers
in
Physics),
Westview
Press,
2003.

S.
Ramaswamy,
Active
Matter,
J.
Stat.
Mech.
Theory
and
Experiment,
Spl.
Issue
on
statphys
26,
2017.

M.
C.
Marchetti,
J.
F.
Joanny,
S.
Ramaswamy,
T.
B.
Liverpool,
J.
Prost,
Madan
Rao,
and
R.
Aditi
Simha,
Hydrodynamics
of
soft
active
matter,
Rev.
Mod.
Phys.
85,
1143
(2013).