In this thesis we use the phase space formulation of quantum mechanics to investigate open quantum systems via the Lindblad equation in the semiclassical limit with a focus on analysing the spread of decoherence. In the case of linear Lindblad operators and quadratic Hamiltonians where the phase space Lindblad equation becomes exact, we find that decoherence is intimately related to H\"{o}rmander's condition which describes when a partial differential equation is hypoelliptic. In particular, it motivates a natural orthogonal decomposition of phase space which encodes the timescales describing the onset of decoherence as well as the subspaces which are protected. Explicit results for the evolution of a Gaussian coherent state and its HilbertSchmidt norm evolving under this exact Lindblad equation are given. We use this to investigate a class of simple examples of networks of harmonic oscillators and show that by changing the macro structure of the network, the spread of decoherence throughout the system can change dramatically. Finally, by interpreting the Lindblad equation as a Schr\"{o}dinger equation on a doubled phase space, we use recent results in the theory of nonHermitian Schr\"{o}dinger equations to determine the evolution of a Gaussian state under a Lindblad equation with general Hamiltonian and Lindblad operators.
Date of Award  23 Jan 2020 

Original language  English 

Awarding Institution   The University of Bristol


Supervisor  Roman C V Schubert (Supervisor) 

 semiclassical
 quantum mechanics
 Lindblad
 decoherence
 phasespace quantum mechanics
 Hörmander
 gaussian states
 coherent states
Semiclassical methods for investigating open quantum systems and decoherence
Plastow, T. (Author). 23 Jan 2020
Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)