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

Knowledge of the content of **PHY302** and **PHY403** is essential to follow this course.

- 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, weak-coupling 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 two-level system in thermal and squeezed thermal bath, Resonance fluorescence, damped harmonic oscillator and Caldeira-Leggett model.
- Non-Markovian quantum processes: Nakajima-Zwanzig projection operator technique, time-convolutionless projection operator method, ex- act solution of the spontaneous decay of a two-level system, Jaynes-Cummings model of resonance.
- Stochastic approach for open quantum systems: Stochastic SchrÃ¶dinger
equation, homodyne photodetection, hetrodyne photodetection, and quan-
tum trajectory approach.

- Markov Chain Mixing, Random Walks on Graphs.

- 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 Fokker-Planck Equations, Springer (2008).
- H. Carmichael, Statistical Methods in Quantum Optics 2: Non-Classical 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, 547â€“607 (1963).