Feynman rules for wave turbulence

Abstract: 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 (the Kolmogorov-Zakharov 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. As a check, we reproduce the next-to-leading order term in the kinetic equation. The correlation functions and corrections to the KZ state that we compute should, in principle, be experimentally measurable quantities.

high energy physicsmathematical physicschaotic dynamicspattern formation and solitonscomputational physicsfluid dynamics

Audience: researchers in the topic

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Georgia Tech CNS Nonlinear Webinar

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