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 underly...

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Main Authors: Creagh, Stephen C., Gradoni, Gabriele, Hartmann, Timo, Tanner, Gregor
Format: Article
Published: IOP 2016
Online Access:https://eprints.nottingham.ac.uk/40811/
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author Creagh, Stephen C.
Gradoni, Gabriele
Hartmann, Timo
Tanner, Gregor
author_facet Creagh, Stephen C.
Gradoni, Gabriele
Hartmann, Timo
Tanner, Gregor
author_sort Creagh, Stephen C.
building Nottingham Research Data Repository
collection Online Access
description 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.
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spelling nottingham-408112020-05-04T18:24:33Z https://eprints.nottingham.ac.uk/40811/ Propagating wave correlations in complex systems Creagh, Stephen C. Gradoni, Gabriele Hartmann, Timo Tanner, Gregor 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. IOP 2016-12-23 Article PeerReviewed Creagh, Stephen C., Gradoni, Gabriele, 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 http://iopscience.iop.org/article/10.1088/1751-8121/50/4/045101/meta doi:10.1088/1751-8121/50/4/045101 doi:10.1088/1751-8121/50/4/045101
spellingShingle Creagh, Stephen C.
Gradoni, Gabriele
Hartmann, Timo
Tanner, Gregor
Propagating wave correlations in complex systems
title Propagating wave correlations in complex systems
title_full Propagating wave correlations in complex systems
title_fullStr Propagating wave correlations in complex systems
title_full_unstemmed Propagating wave correlations in complex systems
title_short Propagating wave correlations in complex systems
title_sort propagating wave correlations in complex systems
url https://eprints.nottingham.ac.uk/40811/
https://eprints.nottingham.ac.uk/40811/
https://eprints.nottingham.ac.uk/40811/