Fokker-Planck approach to wave turbulence
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911051778359296 |
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| author | Schubring, Daniel |
| author_facet | Schubring, Daniel |
| contents | The Kolmogorov-Zakharov stationary states for weak wave turbulence involve solving a leading-order kinetic equation. Recent calculations of higher-order corrections to this kinetic equation using the Martin-Siggia-Rose path integral are reconsidered in terms of stationary states of a Fokker-Planck Hamiltonian. A non-perturbative relation closely related to the quantum mechanical Ehrenfest theorem is introduced and used to express the kinetic equation in terms of divergences of two-point expectation values in the limit of zero dissipation. Similar equations are associated to divergences in higher-order cumulants. It is additionally shown that the ordinary thermal equilibrium state is not actually a stationary state of the Fokker-Planck Hamiltonian, and a non-linear modification of dissipation is considered to remedy this. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08484 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fokker-Planck approach to wave turbulence Schubring, Daniel Statistical Mechanics High Energy Physics - Theory Chaotic Dynamics Fluid Dynamics The Kolmogorov-Zakharov stationary states for weak wave turbulence involve solving a leading-order kinetic equation. Recent calculations of higher-order corrections to this kinetic equation using the Martin-Siggia-Rose path integral are reconsidered in terms of stationary states of a Fokker-Planck Hamiltonian. A non-perturbative relation closely related to the quantum mechanical Ehrenfest theorem is introduced and used to express the kinetic equation in terms of divergences of two-point expectation values in the limit of zero dissipation. Similar equations are associated to divergences in higher-order cumulants. It is additionally shown that the ordinary thermal equilibrium state is not actually a stationary state of the Fokker-Planck Hamiltonian, and a non-linear modification of dissipation is considered to remedy this. |
| title | Fokker-Planck approach to wave turbulence |
| topic | Statistical Mechanics High Energy Physics - Theory Chaotic Dynamics Fluid Dynamics |
| url | https://arxiv.org/abs/2309.08484 |