Propagating wave correlations in complex systems

Creagh, Stephen C.; Gradoni, Gabriele; Hartmann, Timo; Tanner, Gregor

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.

Citation

Creagh, S. C., Gradoni, G., Hartmann, T., & Tanner, G. (2016). Propagating wave correlations in complex systems. Journal of Physics A: Mathematical and Theoretical, 50(4), Article 45101. https://doi.org/10.1088/1751-8121/50/4/045101

• Journal Article Type: Article
• Acceptance Date: Nov 25, 2016
• Publication Date: Dec 23, 2016
• Deposit Date: Feb 27, 2017
• Publicly Available Date: Feb 27, 2017
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 50
• Issue: 4
• Article Number: 45101
• DOI: https://doi.org/10.1088/1751-8121/50/4/045101
• Public URL: https://nottingham-repository.worktribe.com/output/832378
• Publisher URL: http://iopscience.iop.org/article/10.1088/1751-8121/50/4/045101/meta
• 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