Stochastic and Neural Network methods for many-body open quantum systems

Filippo Vicentini

Published Dec 11, 2019• 1 citation

Abstract

This thesis is devoted to the theoretical study of driven-dissipative many-body quantum systems with a particular focus on advanced computational methods. After reviewing several state-of-the-art numerical methods to determine the steady-state and dynamics of open quantum systems described by a Lindblad master equation for the density matrix, this thesis manuscript presents two original methods: (i) an optimal unraveling of stochastic quantum trajectories for disordered systems; (ii) a variational neural network method. The stochastic methods have been applied to investigate the driven-dissipative Bose-Hubbard lattice model that can for instance describe lattices of coupled nonlinear electromagnetic resonators such those obtained with semiconductor microcavities or superconducting quantum circuits. Our study has shown that a critical slowing down of the dynamics occurs for some parameters in dimensions higher than one. The phenomena is linked to a first-order dissipative phase transition and to lattice-level collective bistability. Furthermore, we reveal the role of disorder on the spatial correlation properties of these phenomena. In the last part of the thesis, we present the strong connection between fundamental concepts of machine learning and variational approaches in quantum physics. We present a novel computational method for open quantum systems based on neural network ans\"{a}tze that is compatible with a stochastic minimisation of a cost function through Monte Carlo sampling. As a first application, we have applied this method to the dissipative transverse quantum Ising model. Exciting perspectives and possible developments are also drawn in the concluding remarks.

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