Strong wave turbulence in strongly local large $N$ theories
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 generalized Phillips spectrum (also known as critical balance), or a Kolmogorov-like scaling exponent.
Keywords
Cite
@article{arxiv.2406.18475,
title = {Strong wave turbulence in strongly local large $N$ theories},
author = {Vladimir Rosenhaus and Daniel Schubring},
journal= {arXiv preprint arXiv:2406.18475},
year = {2024}
}