标题： 光的量子流体中的热化：对流扩散方程 显示英文标题

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

摘要： 我们发展了一种关于光量子流体动力学的微观理论，推导出一个动量空间中的有效动力学方程，其形式为对流-扩散方程。 在二维系统且色散为抛物线的情况下，它简化为Bateman--Burgers方程。 流体力学类比将非线性波现象，如激波形成和湍流，与光学腔中光子和极化子的非平衡玻色-爱因斯坦凝聚统一起来。 我们引入雷诺数$(\textit{Re})$并证明凝聚阈值正好对应于单位临界雷诺数$(\textit{Re}=1)$，在此之后$(\textit{Re} > 1)$在动量空间中出现类似激波的前沿，其特征是高动量态中的粒子密度遵循玻色-爱因斯坦分布。 显示英文摘要

摘要： 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.