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Periodically driven quantum systems: some interesting phenomena

Prof. Diptiman Sen, IISc Bangalore

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Abstract:
We discuss some interesting phenomena which can occur when a quantum system is driven periodically in time. The first one is the generation of modes localized at the ends of a one-dimensional tight-binding model when it is subjected to a periodically varying electric field. The end modes can be detected through peaks in the differential conductance across the system. Next, we show that periodic driving with a large amplitude of some operator can give rise to freezing and an emergent conservation law in which the Floquet eigenstates are close to being eigenstates of that operator even when it does not commute with the time-independent part of the Hamiltonian. One also finds the opposite phenomenon of resonances where the Floquet eigenstates deviate strongly from being eigenstates of that operator. Finally, there are some systems which have constraints on the allowed states such that the Hamiltonian has special eigenstates called scar states. When such a system is periodically driven starting with an initial state which has a large overlap with the scar states, correlation functions can show persistent oscillations and the system does not thermalize for a long time. The last two cases show that periodically driven systems may not thermalize for a long time due to various reasons.

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