Fluctuations in a diffusive medium with gain

TL;DR

This paper introduces a stochastic model for amplifying diffusive media, such as random lasers, revealing how fluctuations lead to intermittency and power-law distributions, especially in small or lower-dimensional samples.

Contribution

It derives a stochastic PDE from a simple random-walk model that captures the intermittency and power-law behavior in amplifying diffusive media.

Findings

Intermittency and power-law distributions are predicted by the model.

Features are more prominent in small samples and lower dimensions.

The model provides a theoretical framework for understanding fluctuations in random lasers.

Abstract

We present a stochastic model for amplifying, diffusive media like, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field with contains a multiplicative random-advection term yielding intermittency and power-law distributions of the field itself. Dimensional analysis indicate that such features are more likely to be observed for small enough samples and in lower spatial dimensions.