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Strong wave turbulence in strongly local large- theories
Phys. Rev. E 114, 035101 – Published 1 September, 2026
DOI: https://doi.org/10.1103/p7p2-6f27
Abstract
We study wave turbulence in systems with two special properties: a large number of fields (large ) and a nonlinear interaction that is strongly local in momentum space. The first property allows us to find the kinetic equation at all interaction strengths—both weak and strong, at leading order in . The second allows us to turn the kinetic equation—an integral equation—into a differential equation. We find stationary solutions for the occupation number as a function of wave number, valid at all scales. As expected, on the weak-coupling end, the solutions asymptote to Kolmogorov-Zakharov scaling. On the strong-coupling end, they asymptote to either the widely conjectured critical balance scaling or a Kolmogorov-like scaling exponent.
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