Propagating wave correlations in complex systems

Creagh, Stephen C. and Gradoni, Gabriele and Hartmann, Timo and Tanner, Gregor (2016) Propagating wave correlations in complex systems. Journal of Physics A: Mathematical and Theoretical, 50 (4). 45101/1-45101/18. ISSN 1751-8121

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Abstract

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.

Item Type: Article
Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/1751-8121/50/4/045101
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1088/1751-8121/50/4/045101
Depositing User: Gradoni, Gabriele
Date Deposited: 27 Feb 2017 11:43
Last Modified: 28 Feb 2017 01:44
URI: http://eprints.nottingham.ac.uk/id/eprint/40811

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