Thermalization in Quantum Fluids of Light: A Convection-Diffusion Equation
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 and demonstrate that the condensation threshold corresponds exactly to a critical Reynolds number of unity , beyond which a shock-like front emerges in the momentum space, characterized by the Bose--Einstein distribution for the particle density in states with high momentum.
Cite
@article{arxiv.2501.10537,
title = {Thermalization in Quantum Fluids of Light: A Convection-Diffusion Equation},
author = {Vladislav Yu. Shishkov and Ivan V. Panyukov and Evgeny S. Andrianov and Anton V. Zasedatelev},
journal= {arXiv preprint arXiv:2501.10537},
year = {2025}
}