MC 6460
Candidate
Boris Ragula | Applied Mathematics, University of Waterloo
Title
Numerical Evolution of Correlation Functions With Applications to Dynamically Localized Quantum Fields
Abstract
This thesis presents two topics at the interface between computational physics and Quantum Field Theory (QFT). This first part of the thesis is a comprehensive study of a
numerical evolution scheme for the correlation function of a scalar quantum field. In particular, it explores how one can numerically simulate a bi-scalar function that simultaneously satisfies a time dependent partial differential equation Partial Differential Equations (PDE) in two independent spacetime coordinates. We demonstrate an algorithm that is capable of performing time integration in two time coordinates and yielding convergent numerical results for not only the correlation function, but also for quantities of interest relating to the quantum field. Moreover, we demonstrate a number of methods that can be leveraged to optimize the speed along with the required memory of the algorithm.
The second part of this thesis is concerned with the effects of dynamically localizing the vacuum state of scalar quantum field in (1 + 1)-dimensional Minkowski spacetime. Given recent develops in formulations to a measurement theory for quantum fields, localized field theories have emerged as a potential candidate in developing a relativistically consistent measurement theory. However, concerns have been raised regarding the use of these localized fields in realistic, experimental setups due to the fact that one must dynamically localize the field. The result of this localization would be a loss of purity in the experimentally accessible modes of the field, and thus would not be useful as a measurement device. Utilizing the methods presented in the first part of this thesis, we study the effect of localizing quantum field degrees of freedom by dynamically growing cavity walls through a time-dependent potential. We use our results to show that it is possible to do this without introducing non-negligible mixedness in localized modes of the field. We discuss how this addresses the concerns, raised in previous literature, that the high degree of entanglement of regular states in QFT may hinder relativistic quantum information protocols that make use of localized relativistic probes.