Complexity of waves in nonlinear disordered media

TL;DR

This paper investigates the statistical phase properties of nonlinear coupled modes in disordered media, deriving a phase diagram and discussing implications for phenomena like random lasing and Bose-Einstein condensation.

Contribution

It introduces a Hamiltonian model to analyze phase complexity in nonlinear disordered systems across various randomness and energy levels.

Findings

Complexity varies with temperature and nonlinearity strength.

A phase diagram maps energy and disorder parameters.

Implications for random lasing and Bose-Einstein condensation are discussed.

Abstract

The statistical properties of the phases of several modes nonlinearly coupled in a random system are investigated by means of a Hamiltonian model with disordered couplings. The regime in which the modes have a stationary distribution of their energies and the phases are coupled is studied for arbitrary degrees of randomness and energy. The complexity versus temperature and strength of nonlinearity is calculated. A phase diagram is derived in terms of the stored energy and amount of disorder. Implications in random lasing, nonlinear wave propagation and finite temperature Bose-Einstein condensation are discussed.