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Abstract:

This paper discusses how physics has become globalised in the context of the Oxford Department of Physics and its permanent academic staff over the period from 1987 to 2017. Modern émigrés move to new institutions for scientific opportunities and a physicist will typically work in several over the course of their career.

Abstract:

We characterize the spectrum of the transition matrix for simple random walk on graphs consisting of a finite graph with a finite number of infinite Cayley trees attached. We show that there is a continuous spectrum identical to that for a Cayley tree and, in general, a non-empty pure point spectrum. We apply our results to studying continuous time quantum walk on these graphs. If the pure point spectrum is nonempty the walk is in general confined with a nonzero probability.

Abstract:

In this article, we study two related models of quantum geometry: generic random trees and two-dimensional causal triangulations. The Hausdorff and spectral dimensions that arise in these models are calculated, and their relationship with the structure of the underlying random geometry is explored. Modifications due to interactions with matter fields are also briefly discussed. The approach to the subject is that of classical statistical mechanics, and most of the tools come from probability and graph theory.