Condensation of Classical Nonlinear Waves in a Two-Component System

TL;DR

This paper investigates the formation of large-scale condensates in a two-component classical wave system using coupled nonlinear Schrödinger equations, employing weak turbulence theory to describe the thermodynamics and dynamics of the condensation process.

Contribution

It introduces a comprehensive thermodynamic framework for classical wave condensation in two-component systems, revealing how temperature and condensate fractions depend on initial conditions and energy, with validation through numerical simulations.

Findings

Condensation can occur in one or both components depending on energy levels.

Temperature and condensate fractions are determined by initial particle number and energy.

Numerical simulations agree with the theoretical predictions.

Abstract

We study the formation of large-scale coherent structures (a condensate) for a system of two weakly interacting classical waves. Using the coupled defocusing nonlinear Schr\"odinger (NLS) equations as a representative model, we focus on condensation in the phase mixing regime. We employ weak turbulence theory to provide a complete thermodynamic description of the classical condensation process. We show that the temperature and the condensate mass fractions are fully determined by the total number of particles in each component and the initial total energy. Moreover, we find that, at higher energies, condensation can occur in only one component. The theory presented provides excellent agreement with results of numerical simulations obtained by directly integrating the dynamical model.