Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2003-10-17
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
10 pages, 2 figures
Scientific paper
10.1103/PhysRevE.69.036206
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.
Fyodorov Yan V.
Rozhkov Igor
Weaver Richard L.
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