Bunney, Cameron Richard David
(2024)
Circular motion Unruh effect: in spacetime and in the laboratory.
PhD thesis, University of Nottingham.
Abstract
Quantum Field Theory in Curved Spacetime (QFTCS) is an approximation to the union of General Relativity (GR) and Quantum Field Theory (QFT). Born out of Parker's investigations into cosmological particle creation, QFTCS has since flourished into a productive field in its own right, giving rise to predictions such as black-hole evaporation and the Unruh effect, which states that a uniformly linearly accelerated observer will react to the Minkowski vacuum as if it were a thermal state in temperature T=ℏa/(2πck). Later, in 1981, Unruh demonstrated that acoustic perturbations in a fluid may equivalently be described as a scalar field propagating on a curved spacetime, whose geometry is characterised by the background fluid flow. Furthermore, Unruh found that "the same arguments which lead to black-hole evaporation also predict a thermal spectrum of sound waves should be given out from the sonic horizon in transsonic fluid flow." With this discovery, analogue gravity was born. Over the past forty years, several analogue-gravity and early-Universe simulators have been devised, using physical systems such as ultracold atoms, optical devices, and fluid interfaces. Motivated by the inherent temperature and finite size of the spacetimes provided by these analogue systems, this Thesis extends the theoretical modelling of an accelerated observer to include the effect of thermality and spatial confinement.
Particle detectors in non-inertial motion will register particles in the Minkowski vacuum. A non-inertial trajectory of theoretical and experimental interest is uniform circular motion, in which motion a detector will remain within a finite-size laboratory for an arbitrarily long interaction time. We replace the Minkowski vacuum by a thermal state, breaking the Lorentz invariance of the system and introducing a Doppler effect in the response of the detector. We identify a measure to isolate the acceleration-dependent, rather than velocity-dependent, contribution to the response of a detector. We then apply this modelling to the analogue spacetime provided by thin films of superfluid helium-4 and propose an experiment to extract the observer dependence in the response of a detector probing a quantum field prepared in a thermal state.
We consider the robustness of the duality between an accelerated observer in the Minkowski vacuum and a static observer in a thermal bath by introducing circular motion; we compare the experience of a detector undergoing uniform circular motion through a thermal bath with that of a detector undergoing uniform circular motion whilst linearly accelerating orthogonal to the plane of rotation, known as hypertor motion. Linear acceleration, hypertor motion, and circular motion are all examples of "stationary trajectories", for which motions there exist Unruh-like phenomena. We provide a geometric and algebraic classification of the stationary trajectories in (n+1)-dimensional Minkowski spacetime.
We investigate how the presence of a cylindrical boundary affects the response of a detector undergoing uniform circular motion both through the Minkowski vacuum and through a thermal bath. Our modelling includes the effects of spatial confinement, thermality, a modified dispersion relation, and a finite-time interaction between the quantum field and the detector. We consider the asymptotic behaviour of the response of the detector in the limit of a large boundary. We examine to what extent the spacetimes of constant positive and negative curvature, de Sitter (dS) and anti-de Sitter (AdS) spacetimes, may be considered curved-spacetime analogues of thermality and spatial confinement in the limit of a small cosmological constant and compare with the corresponding results in Minkowski spacetime.
We present two results concerning Bessel functions, which we have not found in the existing literature.
| Item Type: |
Thesis (University of Nottingham only)
(PhD)
|
| Supervisors: |
Louko, Jorma
Weinfurtner, Silke |
| Keywords: |
Circular motion Unruh effect, Unruh effect, Unruh-DeWitt detector, stationary trajectories, Minkowski spacetime, thermal field theory |
| Subjects: |
Q Science > QA Mathematics |
| Faculties/Schools: |
UK Campuses > Faculty of Science > School of Mathematical Sciences |
| Item ID: |
80043 |
| Depositing User: |
Bunney, Cameron
|
| Date Deposited: |
20 Nov 2024 15:56 |
| Last Modified: |
20 Nov 2024 16:08 |
| URI: |
https://eprints.nottingham.ac.uk/id/eprint/80043 |
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