Classical wave experiments on chaotic scattering

Abstract

We review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves. Inasmuch as these experiments use antennas or transducers to couple waves into or out of the systems, scattering theory has to be applied for a quantitative interpretation of the measurements. Most experiments concentrate on tests of predictions from random matrix theory and the random plane wave approximation. In all studied examples a quantitative agreement between experiment and theory is achieved. To this end it is necessary, however, to take absorption and imperfect coupling into account, concepts that were ignored in most previous theoretical investigations. Classical phase space signatures of scattering are being examined in a small number of experiments.

Poincaré recurrences and transient chaos in systems with leaks

“…these two curves is a measure of the error of the naive estimate (13). The general dependence, for δ → 0, is in agreement with the expected δ −D1 relation, by taking into account that D 1 D 0 , where D 0 is the fractal dimension of the attractor.…”

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that properly approximates the width distribution also at large resonance overlap, where the Porter-Thomas result is no longer applicable.Introduction.-Scattering of both classical and quantum waves in systems with chaotic intrinsic dynamics is characterised by universal statistical properties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).…”

Inhomogeneous losses and complexness of wave functions in chaotic cavities

“…Open wave-chaotic systems in the presence of energy losses (absorption) are nowadays under intense experimental and theoretical investigations, see [1,2] for recent reviews as well as [3] for a general discussion. Most of the works concerns the case of uniform absorption which is responsible for homogeneous broadening Γ hom of all the modes (resonance states).…”