Nonlinear Response Of Strongly Interacting Quantum Systems in Nonequilibrium
The recent developments in experimental techniques such as pump-probe spectroscopy, new technologies in building two dimensional materials, and the advent of highly tunable systems in the form of ultracold optical lattices, trapped ionsand array of atoms have opened a new path to investigate the dynamics of strongly correlated system out of equilibrium, which would not be possible with the conventional methods. These new developments not only provided a powerful toolto study some of the most fundamental questions in the nonequilibrium regime of quantum systems but also made it possible to explore new phenomena which have not been observed before. Motivated by some of these experiments,in this thesis, we study a wide range of strongly correlated systems out of equilibrium. We will use a combination of theoretical and computational methods such as sum rules, nonequilibrium Green's function, nonequilibrium dynamical mean-field theory (DMFT), and an exact solution of the non-interacting model to address a wide spectrum of systems out of equilibrium. First, we have generalized a formalism for the nth derivative of a time-dependent operator in theHeisenberg representation and employ it to the spectral sum rules in which we obtain a qualitative understanding of the pump effect on electron-phonon coupling in high Tc superconductors. Then, by using the nonequilibrium DMFTfor the Falicov-Kimball model, we obtain the current-voltage profile of a multilayer device which consists of a single barrier region (usually insulator plane) connected to a number of metallic leads in both sides. To improve the conservationof current and filling across the barrier region, we further develop an optimization method. From a different aspect, we use the DMFT solution of the Falicov-Kimball model to enhance the critical temperature of quantum ordering, which is achallenging problem as the critical temperature lies below currently accessible temperatures. We further propose a few mixtures such as Yb-Cs and Sr-Cs as a possible candidate for detecting the critical temperature enhancementeffect. Finally, in the last chapter, we study some of the most interesting dynamical quantities such as the probability of revivals, the light cone velocity, formation probabilities and Shannon information in the XY chain.Although XY chain is a free fermionic system, it has been considered as one of the most interesting models from both theoretical and experimental views. Because this model, not only manifests a quantum phase transition but it has been the subject ofthe array of trapped ions and neutral atoms which are the most promising candidates for a quantum simulator. We show that the formation probabilities, revival probabilities, and observed propagation velocity are actually state-dependentand non-trivially predictable in the XY chain.
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Cohn, Jeffrey (Georgetown University, 2019)Exact simulation of quantum systems is intractable on current classical computers due to the time required to calculate the exponential number of amplitudes which represent a quantum state. This thesis explores how highly ...