arXiv subjects

Stephen C Creagh

Publications and source records attributed to Stephen C Creagh.

3 recordsLinked to original sources

arXiv2017

Propagating wave correlations in complex systems

We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local mean of these correlation functions in terms of the underlying classical dynamics. By defining appropriate ensemble averages, we show that fluctuations about the mean can be characterised in terms of classical correlations. We give in particular an explicit expression relating fluctuations of diagonal contributions to those of the full wave correlation function. The methods have a wide range of applications both in quantum mechanics and for classical wave problems such as in vibro-acoustics and electromagnetism. We apply the methods here to simple quantum systems, so-called quantum maps, which model the behaviour of generic problems on Poincaré sections. Although low-dimensional, these models exhibit a chaotic classical limit and share common characteristics with wave propagation in complex structures.

nlin.CD↗

arXiv2013

In-out decomposition of boundary integral equations

We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features such as diffraction and evanescent coupling; these effects are absent in the well known semiclassical transfer operators in the sense of Bogomolny. It has long been established that transfer operators are equivalent to the boundary integral approach within semiclassical approximation. Exact treatments have been restricted to specific boundary conditions (such as Dirichlet or Neumann). The approach we propose is independent of the boundary conditions, and in fact allows one to decouple entirely the problem of propagating waves across the interior from the problem of reflecting waves at the boundary. As an application, we show how the decomposition may be used to calculate Goos-Hänchen shifts of ray dynamics in billiards with variable boundary conditions and for dielectric cavities.

physics.class-ph↗

arXiv2007

Directional emission from weakly eccentric resonators

It is shown that when a circular resonator is deformed in a nonintegrable way, a symmetry breaking of escaping rays occurs which can dramatically modulate the outgoing wave even for small perturbations. The underlying mechanism does not occur in integrable models for which the ray families can be computed exactly and is described in this Letter on the basis of canonical perturbation theory. Emission from deformed resonators is currently of immense practical interest in the context of whispering-gallery optical resonances of dielectric cavities and the approach outlined here promises simple analytical characterisations in the important case of small deformations.

nlin.CD↗