An Equation of State for Turbulence in the Gross-Pitaevskii model
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| author | Martirosyan, Gevorg Fujimoto, Kazuya Navon, Nir |
| author_facet | Martirosyan, Gevorg Fujimoto, Kazuya Navon, Nir |
| contents | We report the numerical observation of a far-from-equilibrium equation of state (EOS) in the Gross-Pitaevskii model. We first show that the momentum distribution of the turbulent cascade is well described by wave-turbulent kinetic theory in the appropriate limits. Calculating the energy and particle fluxes $Π_\varepsilon(k)$ and $Π_N(k)$, we show that the turbulent state possesses the hallmarks of a direct energy cascade. Building on this, we show that the GP model encodes a universal EOS in the form of a relationship between the turbulent cascade's momentum distribution amplitude $n_0$ and the energy flux $ε$ in the steady state. We find that in our regime of `mixed' turbulence - where both vortices and waves play a significant role - $n_0\propto ε^{0.67(2)}$, a result that is not captured by any existing theory of turbulence but that agrees with a recent experimental measurement for large energy fluxes. Finally, we find that the concept of quasi-static thermodynamic processes between equilibrium states extends to far-from-equilibrium steady states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Equation of State for Turbulence in the Gross-Pitaevskii model Martirosyan, Gevorg Fujimoto, Kazuya Navon, Nir Quantum Gases Statistical Mechanics Atomic Physics Fluid Dynamics We report the numerical observation of a far-from-equilibrium equation of state (EOS) in the Gross-Pitaevskii model. We first show that the momentum distribution of the turbulent cascade is well described by wave-turbulent kinetic theory in the appropriate limits. Calculating the energy and particle fluxes $Π_\varepsilon(k)$ and $Π_N(k)$, we show that the turbulent state possesses the hallmarks of a direct energy cascade. Building on this, we show that the GP model encodes a universal EOS in the form of a relationship between the turbulent cascade's momentum distribution amplitude $n_0$ and the energy flux $ε$ in the steady state. We find that in our regime of `mixed' turbulence - where both vortices and waves play a significant role - $n_0\propto ε^{0.67(2)}$, a result that is not captured by any existing theory of turbulence but that agrees with a recent experimental measurement for large energy fluxes. Finally, we find that the concept of quasi-static thermodynamic processes between equilibrium states extends to far-from-equilibrium steady states. |
| title | An Equation of State for Turbulence in the Gross-Pitaevskii model |
| topic | Quantum Gases Statistical Mechanics Atomic Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2407.08738 |