Variance of transmitted power in multichannel dissipative ergodic structures invariant under time reversal

TL;DR

This paper employs random matrix theory and supersymmetry techniques to accurately analyze the variance of transmitted wave power in ergodic, time-reversal invariant systems with dissipation, clarifying discrepancies with experimental data.

Contribution

It introduces an exact RMT-based method using supersymmetry to analyze wave power transmission, improving upon naive statistical assumptions.

Findings

Supersymmetry approach yields more accurate results than naive assumptions.

Monte Carlo simulations confirm the supersymmetric calculations.

Results help explain discrepancies between theory and ultrasonic experiments.

Abstract

We use random matrix theory (RMT) to study the first two moments of the wave power transmitted in time reversal invariant systems having ergodic motion. Dissipation is modeled by a number of loss channels of variable coupling strength. To make a connection with ultrasonic experiments on ergodic elastodynamic billiards, the channels injecting and collecting the waves are assumed to be negligibly coupled to the medium, and to contribute essentially no dissipation. Within the RMT model we calculate the quantities of interest exactly, employing the supersymmetry technique. This approach is found to be more accurate than another method based on simplifying naive assumptions for the statistics of the eigenfrequencies and the eigenfunctions. The results of the supersymmetric method are confirmed by Monte Carlo numerical simulation and are used to reveal a possible source of the disagreement between the predictions of the naive theory and ultrasonic measurements.