The effect of short ray trajectories on the scattering statistics of wave chaotic systems

TL;DR

This paper explores how short ray trajectories influence the scattering statistics of wave chaotic systems, linking classical trajectories with quantum scattering properties through semiclassical calculations.

Contribution

It introduces a method to express the average impedance matrix in terms of classical trajectories, enhancing the understanding of system-specific effects in wave chaos.

Findings

The average impedance matrix can be semiclassically computed from classical trajectories.

Theoretical predictions align well with numerical simulations.

Short ray trajectories significantly impact scattering statistics.

Abstract

In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system specific information into the statistical model, such as the introduction of the average scattering matrix in the Poisson kernel. Here it is shown that the average impedance matrix, which also characterizes the system-specific properties, can be expressed in terms of classical trajectories that travel between ports and thus can be calculated semiclassically. Theoretical results are compared with numerical solutions for a model wave-chaotic system.