Weller-Davies, Zachary;
(2024)
Classical-quantum dynamics with applications to gravity.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
We develop autonomous classical-quantum dynamics by providing formalism and tools to study effective theories of interacting classical and quantum systems. We find the most general form of continuous classical-quantum master equation, which generalizes the Fokker-Planck equation of classical mechanics and the Lindblad equation of open quantum systems, allowing for coupling between the classical and quantum systems. We further show that this master equation can be unraveled by stochastic classical-quantum trajectories. The resulting dynamics is a natural generalization of the standard semi-classical equations of motion. However, because the dynamics are linear in the combined classical-quantum state, they are completely positive on all initial quantum states, providing a method to study semi-classical physics even in the presence of large quantum fluctuations. We find a general path integral representation for classical-quantum dynamics, generalizing the Feynman-Vernon and classical stochastic path integrals, allowing for interaction between classical and quantum systems. Via path integral methods, we give the first examples of Lorentz invariant classical-quantum dynamics. We further find diffeomorphism invariant classical-quantum theories of gravity. We provide a methodology to derive the generalizations of the gravitational Hamiltonian and momentum constraints in such theories. We prove that the consistency of classical-quantum coupling implies a general trade-off between the quantum decoherence rate and the degree of diffusion induced in the classical system, given by the back-reaction strength. Applying the trade-off relation to Newtonian gravity, we find an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place substantial restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter, with part of the parameter space of such theories already squeezed out. We provide figures of merit that can be used in future experiments.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Classical-quantum dynamics with applications to gravity |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2024. 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/10193630 |
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