Theoritical study of driven correlated quantum matter - Bhaskar, Mukherjee
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Periodically driven closed quantum many-body systems have become an active field of research nowadays. The drive frequency, in such systems, is an important parameter since it can be tuned to realize several interesting phenomena that have no analog in equilibrium systems. A systematic theoretical understanding of such phenomena has already been achieved in highfrequency regime using inverse frequency perturbation expansions. These kinds of expansion diverge in the low-frequency region where it is difficult to find any semi-analytic techniques. The purpose of this thesis is to establish a…mehr

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Periodically driven closed quantum many-body systems have become an active field of research nowadays. The drive frequency, in such systems, is an important parameter since it can be tuned to realize several interesting phenomena that have no analog in equilibrium systems. A systematic theoretical understanding of such phenomena has already been achieved in highfrequency regime using inverse frequency perturbation expansions. These kinds of expansion diverge in the low-frequency region where it is difficult to find any semi-analytic techniques. The purpose of this thesis is to establish a framework which works well for low to moderate drive frequencies. Adiabatic-impulse approximation which we develop in this thesis provides such a technique. We show that this method with proper modifications can be successfully applied to describe many features of low-frequency phase diagram of periodically driven non-interacting system like irradiated graphene in frequency(¿)-amplitude(A0) plane. We compute phase bands of such system which are the eigenphases of corresponding time-evolution operator U(t, 0) using adiabatic-impulse theory. We show that these results match extremely well with exact numerical calculations in the low drive frequency region. We also show that in systems like interacting bosons placed in a strong electric field the phenomena of dynamic freezing can be enhanced by driving more than one parameter of the Hamiltonian at some specific ratio of drive frequencies. This phenomenon is understood as Stuckelberg interference of few instantaneous energy levels in the many-body spectrum, undergoing exact level crossing. We also study dynamics of driven systems in the presence of stochastic resets. We find that such resets at random times result in a novel steady value of reset averaged observables. On the other hand, stochastic noise in the vector potential of an incident electromagnetic wave may drastically change the phase band structure of irradiated systems at some specific crystal momentum points in the Brillouin-zone. We numerically show that self- averaging limit exists in such noisy dynamical systems and the modifications in the phase band structure can be understood by analyzing the noise averaged Hamiltonian.