1 December 2021 Wed 5 pm

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We study two classes of open systems: discrete-time quantum walks (a type of Floquet-engineered discrete quantum map) and the Lindblad master equation (a general framework of dissipative quantum systems), focusing on the non-equilibrium properties of these systems. We study localization and delocalization phenomena, soliton-like excitations, and quasi-stationary properties of  open quantum systems.

In discrete-time quantum walks we study both analytically and numerically Anderson localization induced by disorder in several physically relevant fields. In particular, we show the existence of a regime with a uniform localization length value for every eigenstate and give an analytical expression for it. Based on this, we study wave packet spreading due to mean-field-like nonlinearity in presence of a random field, and confirm previous conjectures on this dynamics numerically up to previously unachievable time scales. We further study the effect of nonlinearity in an all-bands-flat setup. In this setup, the particle transport is only carried by nonlinearity. We show the existence of a plethora of both stationary and moving soliton-like solutions and analyze their stability.

In the framework of the Lindblad master equation, we continue research of localization properties and study signatures of many-body localization transition in the presence of dissipation. We show that the inclusion of engineered dissipation allows for detection of the transition in both dynamical -- growth of entanglement rate; and steady-state properties -- statistics of local observables, average entanglement entropy, and spectral statistics. Moreover, we show that engineered dissipation can prevent dephasing from completely removing traces of the Hamiltonian properties in the steady-state. For this study, we develop an efficient parallel supercomputer implementation of the time-evolving block decimation algorithm, that is used for the evolution of many-body dissipative 1D systems. Furthermore, we study quasi-stationary states in Lindblad systems by generalizing a well-known classical approach for Markovian processes. We derive projected Lindblad equation and propose a generalized quantum trajectories algorithm for efficient simulation of systems with quasi-stationary properties.

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