Thermalization in Quantum Fluids of Light: A Convection-Diffusion Equation
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909460548550656 |
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| author | Shishkov, Vladislav Yu. Panyukov, Ivan V. Andrianov, Evgeny S. Zasedatelev, Anton V. |
| author_facet | Shishkov, Vladislav Yu. Panyukov, Ivan V. Andrianov, Evgeny S. Zasedatelev, Anton V. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermalization in Quantum Fluids of Light: A Convection-Diffusion Equation Shishkov, Vladislav Yu. Panyukov, Ivan V. Andrianov, Evgeny S. Zasedatelev, Anton V. Quantum Gases 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. |
| title | Thermalization in Quantum Fluids of Light: A Convection-Diffusion Equation |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2501.10537 |