Non-linear supersymmetric Sigma-Model for Diffusive Scattering of Classical Waves with Resonance Enhancement

TL;DR

This paper develops a non-linear sigma-model for classical wave transport in disordered media, compares it with electronic models, and extends it to include resonance scattering, aligning theoretical predictions with experimental data.

Contribution

The paper introduces a non-linear sigma-model for classical wave diffusion and generalizes it to account for resonance scattering effects.

Findings

The model's effective action form remains unchanged with resonance inclusion.

Resonance scattering modifies the mean level density parameter.

The extended model aligns well with experimental observations.

Abstract

We derive a non-linear sigma-model for the transport of light (classical waves) through a disordered medium. We compare this extension of the model with the well-established non-linear sigma-model for the transport of electrons (Schroedinger waves) and display similarities of and differences between both cases. Motivated by experimental work (M. van Albada et al., Phys. Rev. Lett. 66 (1991) 3132), we then generalize the non-linear sigma-model further to include resonance scattering. We find that the form of the effective action is unchanged but that a parameter of the effective action, the mean level density, is modified in a manner which correctly accounts for the data.