Discrete time quantum walks : from synthetic gauge fields to spontaneous equilibration

Abstract : Problems too demanding for classical computers can be approached promisingly with quantum simulators, which operate using one controllable quantum system in order to investigate the behavior and properties of a less accessible one. Over the past few years, significant progress has been made in a number of experimental and theoretical fields. Quantum Walks (QWs) are simple and sophisticated discrete space and time dynamical systems and it has been shown that in the continuous limit different emergent quantum fields can be simulated. In this thesis we will draw on QWs to further explore various areas of interest in Physics. More specifically our analysis will branch out into three main directions: (i) the connection between QWs and quantum field theory, with particular attention to bridging the quantum coin of QWs with the geometrical properties of gauge field theories; (ii) the study of QWs' classical limit and of the transient semi-classical dynamics, especially in relation with field theories; (iii) the spontaneous equilibration and thermalization in some nonlinear QWs-like models. Every step of this thesis will be validated by specific analytical results and numerical implementations.
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Submitted on : Thursday, November 19, 2015 - 11:12:10 AM
Last modification on : Thursday, May 16, 2019 - 5:43:18 PM
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Giuseppe Di Molfetta. Discrete time quantum walks : from synthetic gauge fields to spontaneous equilibration. Physics [physics]. Université Pierre et Marie Curie - Paris VI, 2015. English. ⟨NNT : 2015PA066220⟩. ⟨tel-01230891⟩

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