Quantum Trajectories: Metastability, Gauge Freedom and Weak Symmetries
type: CreativeWork
description: This thesis considers quantum systems which interact with their surrounding environment. Specifically we consider the underlying stochastic dynamics which arise from the back-action of measurements performed in the environment. These quantum trajectories can be tracked by continuously monitoring the environment, as is now possible in modern experiments. We consider phenomena understood at the average level of the system state density matrix, and explore these at this more information rich level. This is especially relevant for experimental setups and implementation of quantum technologies. Firstly, we consider how systems exhibiting metastability behave at the level of stochastic quantum trajectories. In doing so we make comparisons to classical theories of metastability, where trajectories exhibit fast relaxation into distinct phases and slow transitions between them. We also illustrate when this phenomenology does not hold, with instead the emergence of a slow manifold in the form of a decoherence free subspace. We also highlight the useful role that quantum reset processes can play in the analysis of stochastic quantum trajectories. The dynamics of the stochastic quantum trajectories depends on the choice of environmental measurements. There are many choices which leave the average dynamics unchanged, but give different statistical ensembles of quantum trajectories. This gauge freedom of the average dynamics is well known. We derive the analogous result at the level of quantum trajectory ensembles; giving the measurement protocols which leave the generator of the stochastic trajectory dynamics unchanged. We also extend this to include joint trajectories of conditional system states and their associated measurement records, either full records or coarse-grained. Using these results on gauge freedoms of quantum trajectories, we consider the conditions under which the trajectory dynamics exhibit a weak unitary symmetry. We then consider under what conditions the joi…
abstract: This thesis considers quantum systems which interact with their surrounding environment. Specifically we consider the underlying stochastic dynamics which arise from the back-action of measurements performed in the environment. These quantum trajectories can be tracked by continuously monitoring the environment, as is now possible in modern experiments. We consider phenomena understood at the average level of the system state density matrix, and explore these at this more information rich level. This is especially relevant for experimental setups and implementation of quantum technologies. Firstly, we consider how systems exhibiting metastability behave at the level of stochastic quantum trajectories. In doing so we make comparisons to classical theories of metastability, where trajectories exhibit fast relaxation into distinct phases and slow transitions between them. We also illustrate when this phenomenology does not hold, with instead the emergence of a slow manifold in the form of a decoherence free subspace. We also highlight the useful role that quantum reset processes can play in the analysis of stochastic quantum trajectories. The dynamics of the stochastic quantum trajectories depends on the choice of environmental measurements. There are many choices which leave the average dynamics unchanged, but give different statistical ensembles of quantum trajectories. This gauge freedom of the average dynamics is well known. We derive the analogous result at the level of quantum trajectory ensembles; giving the measurement protocols which leave the generator of the stochastic trajectory dynamics unchanged. We also extend this to include joint trajectories of conditional system states and their associated measurement records, either full records or coarse-grained. Using these results on gauge freedoms of quantum trajectories, we consider the conditions under which the trajectory dynamics exhibit a weak unitary symmetry. We then consider under what conditions the joi…
author: Brown, Calum
language: eng
keywords: Open Quantum Systems, Quantum Trajectories, Stochastic Quantum Dynamics, Metastability, Weak Symmetry, Statistical Physics
license: https://www.repository.cam.ac.uk/bitstreams/e62bdac6-e655-482c-be61-65df6ea01047/download
license: http://purl.org/NET/rdflicense/allrightsreserved
date published: 2025-09-29
date modified: 2026-07-24T01:33:23Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.128044