Feynman rules for forced wave turbulence
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929286757220352 |
|---|---|
| author | Rosenhaus, Vladimir Smolkin, Michael |
| author_facet | Rosenhaus, Vladimir Smolkin, Michael |
| contents | It has long been known that weakly nonlinear field theories can have a late-time stationary state that is not the thermal state, but a wave turbulent state with a far-from-equilibrium cascade of energy. We go beyond the existence of the wave turbulent state, studying fluctuations about the wave turbulent state. Specifically, we take a classical field theory with an arbitrary quartic interaction and add dissipation and Gaussian-random forcing. Employing the path integral relation between stochastic classical field theories and quantum field theories, we give a prescription, in terms of Feynman diagrams, for computing correlation functions in this system. We explicitly compute the two-point and four-point functions of the field to next-to-leading order in the coupling. Through an appropriate choice of forcing and dissipation, these correspond to correlation functions in the wave turbulent state. In particular, we derive the kinetic equation to next-to-leading order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_08168 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Feynman rules for forced wave turbulence Rosenhaus, Vladimir Smolkin, Michael Statistical Mechanics High Energy Physics - Theory Chaotic Dynamics Fluid Dynamics It has long been known that weakly nonlinear field theories can have a late-time stationary state that is not the thermal state, but a wave turbulent state with a far-from-equilibrium cascade of energy. We go beyond the existence of the wave turbulent state, studying fluctuations about the wave turbulent state. Specifically, we take a classical field theory with an arbitrary quartic interaction and add dissipation and Gaussian-random forcing. Employing the path integral relation between stochastic classical field theories and quantum field theories, we give a prescription, in terms of Feynman diagrams, for computing correlation functions in this system. We explicitly compute the two-point and four-point functions of the field to next-to-leading order in the coupling. Through an appropriate choice of forcing and dissipation, these correspond to correlation functions in the wave turbulent state. In particular, we derive the kinetic equation to next-to-leading order. |
| title | Feynman rules for forced wave turbulence |
| topic | Statistical Mechanics High Energy Physics - Theory Chaotic Dynamics Fluid Dynamics |
| url | https://arxiv.org/abs/2203.08168 |