Transmission and localization in connected ergodic reverberation rooms

Abstract

The wave power redistribution in two connected reverberant structures represents a paradigm problem in studies of transmission through a complex structure consisting of several reverberant substructures. We analyze randomly coupled ergodic reverberation rooms with the goal to extend such analysis to a more general situation. The two-room problem is, however, quite challenging on its own [R. L. Weaver and O. I. Lobkis, J. Sound Vibr. 231, 1111–1134 (2000)]. Although the ergodicity assumption allows one to use random matrix theory (RMT), by describing both subsystems with random Gaussian Hamiltonians, the nonperturbative calculations of power transmission and localization have not yet been done. The only attempt made in this direction was the corresponding study of two coupled quantum dots [A. Tschersich and K. B. Efetov, Physi. Rev. E 62, 2042–2045 (2000)], which used the supersymmetry technique to calculate the joint distribution of local densities of electron wavefunctions and found spatial correlations absent in a single chaotic system. Here, we present both perturbative and nonperturbative (in ensemble averaging) RMT calculations of simplest nontrivial characteristics of power transmission and localization, and compare it with numerics.