Thermalization in Quantum Fluids of Light: A Convection-Diffusion Equation

TL;DR

This paper develops a microscopic kinetic theory for quantum fluids of light, linking nonlinear wave phenomena and Bose--Einstein condensation through a convection-diffusion framework, and identifies a critical Reynolds number for condensation.

Contribution

It introduces a novel kinetic equation for quantum light fluids that unifies hydrodynamic phenomena with quantum condensation, revealing a critical Reynolds number for phase transition.

Findings

Derivation of a convection-diffusion equation for quantum light dynamics

Identification of a critical Reynolds number (Re=1) for Bose--Einstein condensation

Prediction of shock-like fronts in momentum space beyond Re=1

Abstract

We develop a microscopic theory for the dynamics of quantum fluids of light, deriving an effective kinetic equation in momentum space that takes the form of the convection-diffusion equation. In the particular case of two-dimensional systems with parabolic dispersion, it reduces to the Bateman--Burgers equation. The hydrodynamic analogy unifies nonlinear wave phenomena, such as shock wave formation and turbulence, with non-equilibrium Bose--Einstein condensation of photons and polaritons in optical cavities. We introduce the Reynolds number $(\textit{Re})$ and demonstrate that the condensation threshold corresponds exactly to a critical Reynolds number of unity $(\textit{Re}=1)$, beyond which $(\textit{Re} > 1)$ a shock-like front emerges in the momentum space, characterized by the Bose--Einstein distribution for the particle density in states with high momentum.