Predicting the statistics of wave transport through chaotic cavities by the random coupling model: A review and recent progress

Abstract

In this review, a model (the Random Coupling Model) that gives a statistical description of the coupling of radiation into and out of large enclosures through localized and/or distributed channels is presented. The Random Coupling Model combines both deterministic and statistical phenomena. The model makes use of wave chaos theory to extend the classical modal description of the cavity fields in the presence of boundaries that lead to chaotic ray trajectories. The model is based on a clear separation between the universal statistical behavior of the isolated chaotic system, and the deterministic coupling channel characteristics. Moreover, the ability of the random coupling model to describe interconnected cavities, aperture coupling, and the effects of short ray trajectories is discussed. A relation between the random coupling model and other formulations adopted in acoustics, optics, and statistical electromagnetics, is examined. In particular, a rigorous analogy of the random coupling model with the Statistical Energy Analysis used in acoustics is presented.

Resonance width distribution in RMT: Weak-coupling regime beyond Porter-Thomas

“…We show that to the leading order in weak coupling the perturbative χ 2 M distribution of the resonance widths (in particular, the Porter-Thomas distribution at M = 1) should be corrected by a factor related to a certain average of the ratio of square roots of the characteristic polynomial ('spectral determinant') of the underlying RMT Hamiltonian. A simple single-channel expression is obtained that properly approximates the width distribution also at large resonance overlap, where the Porter-Thomas result is no longer applicable.Introduction.-Scattering of both classical and quantum waves in systems with chaotic intrinsic dynamics is characterised by universal statistical properties [1][2][3]. Those can be understood by studying the properties of quasi-stationary states in an open system formed at the intermediate stage of the scattering process [4][5][6][7].…”

“…Introduction.-Scattering of both classical and quantum waves in systems with chaotic intrinsic dynamics is characterised by universal statistical properties [1][2][3]. Those can be understood by studying the properties of quasi-stationary states in an open system formed at the intermediate stage of the scattering process [4][5][6][7].…”

“…In many realistic situations, however, the opening is small ("quantum") in the sense that it does not scale with the system size and supports at a given energy only a finite p-1 1 Dmitry V. Savin 2,3 number M of scattering channels. Representative examples are microwave cavities [1] (where M is just the number of the attached antennas) and quantum dots [38] (then M is fixed by transverse quantisation for the modes propagating in the leads).…”

Experimental Study of Quantum Graphs with Simple Microwave Networks: Non-Universal Features

“…The random coupling model (RCM) describes the coupling of radiation into and out of electrically large enclosures with chaotic ray dynamics [8]. The RCM gives a prescription for determining both the universal and non-universal features of the experiment.…”

“…The random coupling model (RCM) [8] has been introduced to describe the impedance statistics of singleand multi-port wave chaotic systems. In this work we compare the predictions of the RCM with our measurements of an ensemble of tetrahedral graphs.…”