Propagating wave correlations in complex systems. (23rd December 2016)

• Record Type: Journal Article
• Authors: Creagh, Stephen C; Gradoni, Gabriele; Hartmann, Timo; Tanner, Gregor
• Is Part Of: Journal of physics. Volume 50:Number 4(2017)
• Publication Date: 2016-12-23
• Subjects: semiclassical theories -- wave chaos -- Wigner transformation -- wave fluctuations -- high frequency asymptotics; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/50/4/045101
• Languages: English
• ISSNs: 1751-8113

Abstract

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.