Phase space dynamics of non-Hermitian quantum systems
File(s)
Author(s)
Holmes, Katherine
Type
Thesis
Abstract
In this thesis, we shall study phase space dynamics of non-Hermitian quantum systems in the semiclassical limit. I derive the (semi)classical dynamics generated by non-Hermitian Hamiltonians from quantum dynamical equations for two quasiprobability distributions, the Husimi and Wigner distributions. The methodology presented applies to generic Hamiltonians expressed as power series of n-dimensional position and momentum operators and the quasi-probability distributions are allowed to have arbitrary initial conditions. In the Husimi and Wigner representations, we uncover an important function, the norm landscape, contained within the classical dynamics, which evolves over time and phase space. The norm landscape
describes the classical analogue of loss and gain, a fundamental characteristic of non-Hermitian system.
This thesis analyses the quantum and classical phase space dynamics of several examples of non-Hermitian systems. The examples include linear systems, which in some cases have exact analytic solutions in either the Husimi or Wigner representation; non-linear systems, including a dissipative and a PT-symmetric Hamiltonian, and a two-dimensional billiard model. The conclusion of the thesis summarises preliminary results for further research projects.
describes the classical analogue of loss and gain, a fundamental characteristic of non-Hermitian system.
This thesis analyses the quantum and classical phase space dynamics of several examples of non-Hermitian systems. The examples include linear systems, which in some cases have exact analytic solutions in either the Husimi or Wigner representation; non-linear systems, including a dissipative and a PT-symmetric Hamiltonian, and a two-dimensional billiard model. The conclusion of the thesis summarises preliminary results for further research projects.
Version
Open Access
Date Issued
2025-01-10
Date Awarded
01/09/2025
Advisor
Graefe, Eva-Maria
Sponsor
Imperial College London
Publisher Department
Department of Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)