Statistics of transmitted power in multichannel dissipative ergodic structures

TL;DR

This paper applies Random Matrix Theory to analyze the distribution and moments of wave power transmission in ergodic, dissipative multichannel systems, providing new analytical approaches and confirming results through simulations.

Contribution

It introduces two analytical methods for studying wave power transmission in dissipative ergodic systems, with validation via numerical simulations.

Findings

Supersymmetry method accurately predicts power distribution.

Simpler RMT-based technique effective for systems with uniform dissipation.

Results applicable to open and closed dissipative ergodic structures.

Abstract

We use the Random Matrix Theory (RMT) to study the probability distribution function and moments of the wave power transmitted inside systems with ergodic wave motion. The results describe either open multichannel systems or their closed counterparts with local-in-space internal dissipation. We concentrate on the regime of broken time-reversal invariance and employ two different analytical approaches: the exact supersymmetry method and a simpler technique that uses RMT eigenstatistics for closed non-dissipative systems as an input. The results of the supersymmetric method were confirmed by numerical simulation. The simpler method is found to be adequate for closed systems with uniform dissipation, or in the limit of a large number of weak local dampers.