The Effect of Resonances on Diffusive Scattering

TL;DR

This paper extends random matrix theory to include resonances, analyzing their impact on diffusive scattering of light and electrons, revealing how resonances alter the diffusion constant and density of states.

Contribution

It introduces a generalized theoretical framework incorporating resonances into random matrix theory, providing analytical calculations of spectral properties and diffusion behavior.

Findings

Resonances cause a dip in the mean level spacing.

The diffusion constant scales with the effective mean level spacing.

The theory explains experimental light scattering results with resonant scatterers.

Abstract

The presence of resonances modifies the passage of light or of electrons through a disordered medium. We generalize random matrix theory to account for this effect. Using supersymmetry, we calculate analytically the mean density of states, and the effective Lagrangean of the generating functional for the two-point function. We show that the diffusion constant scales with the effective mean level spacing. The latter exhibits a resonance dip. These facts allow us to interpret experimental results on light scattering for different concentrations of resonant scatterers.