Non-equilibrium Dynamics of Driven Low-dimensional Quantum Systems
Author | : Stefano Scopa |
Publisher | : |
Total Pages | : 0 |
Release | : 2019 |
ISBN-10 | : OCLC:1136902408 |
ISBN-13 | : |
Rating | : 4/5 ( Downloads) |
Download or read book Non-equilibrium Dynamics of Driven Low-dimensional Quantum Systems written by Stefano Scopa and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis analyzes some aspects regarding the dynamics of one-dimensional quantum systems which are driven out-of-equilibrium by the presence of time- dependent external fields. Among the possible kinds of driven systems, our focus is dedicated to the slow variation of a Hamiltonian's parameter across a quantum phase transition and to the case of a time-periodic forcing. To begin with, we prepare the background and the tools needed in the following. This includes a brief introduction to quantum critical models (in particular to the xy spin chain and to the Bose-Hubbard model), the Kibble-Zurek mechanism and Floquet theory. Next, we consider the non-equilibrium dynamics of Tonks-Girardeau gases in time-dependent harmonic trap potentials. The analysis is made with different techniques: perturbative expansions, numerical exact diagonalization and exact methods based on the theory of Ermakov-Lewis dynamical invariants. The last part of the thesis deals instead with the non-equilibrium dynamics of markovian open quantum systems subject to time-periodic perturbations of the system parameters and of the environment. This has led to an exact formulation of Floquet theory for a Lindblad dynamics. Moreover, within the Lindblad-Floquet framework it is possible to have an exact characterization ofthe finite-time operation of quantum heat-engines.