Feynman rules for forced wave turbulence

Vladimir Rosenhaus*, Michael Smolkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageAmerican English
Article number142
JournalJournal of High Energy Physics
Issue number1
StatePublished - Jan 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).


  • Field Theory Hydrodynamics
  • Non-Equilibrium Field Theory
  • Thermal Field Theory


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