Effective theories of classical-quantum dynamics

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Effective theories of classical-quantum dynamics

Layton, Isaac; (2025) Effective theories of classical-quantum dynamics. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

In this work, we study systems operating in a regime where a partially classical, partially quantum effective description is valid. Our central focus is provided by a recently characterised general form of classical-quantum dynamics, which allows for a consistent treatment of classical-quantum systems in terms of both stochastic unravellings and linear master equations. We first show that these dynamics provide a consistent version of the mean-field and reversible bracket approaches to backreaction, which we use to provide a precise regime of validity to standard semi-classical approaches. Utilising partial versions of the W, Q and P quasiprobability representations, we then show that these dynamics can be derived from quantum theory in the classical limit of a quantum subsystem strongly decohered by its environment. Finding the general necessary and sufficient conditions for classical-quantum detailed balance, we then construct a class of dynamics that allow the thermal state of the combined classical-quantum system to be preserved, which we use to prove the second law of thermodynamics for classical-quantum systems. Aside from the three fundamental classes of effective classical-quantum dynamics we introduce, we provide a number of technical tools important to their study, such as characterising when the quantum system remains pure conditioned on the classical trajectory. We illustrate our findings by introducing several models, including an analytically solvable model of a one-dimensional classical system coupled to a qubit, and a numerically solvable model of a classical-quantum oscillator system that exhibits thermalisation. This work provides the foundations for general studies of non-relativistic models of effective classical-quantum systems in a variety of contexts, from continuous quantum measurement to molecular dynamics.

Type:	Thesis (Doctoral)
Qualification:	Ph.D
Title:	Effective theories of classical-quantum dynamics
Open access status:	An open access version is available from UCL Discovery
Language:	English
Additional information:	Copyright © The Author 2025. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request.
UCL classification:	UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI:	https://discovery.ucl.ac.uk/id/eprint/10204902