Kinetic Equations and Turbulence in Large N Vector and SYK-like Models
Abstract
We apply large N expansion techniques to derive kinetic equations for strongly coupled, far-from-equilibrium field theories with O(N) symmetry. For large N vector models, the quasi-classical approximation holds. Incorporating arbitrary momentum-dependent interactions, we show the dynamics obey the standard kinetic equation, with the scattering amplitude given by the retarded propagator of the auxiliary Hubbard-Stratonovich field. This has broad applications to systems like spin wave and Langmuir ion-acoustic turbulence. For large N random coupling (SYK-like) models in d dimensions, leading-order melon diagrams induce order-one propagator renormalization and finite spectral width. The corresponding kinetic equation, unlike those for standard weakly interacting systems, does not have a local-in-time collision integral. We find evidence for a stationary, scale-invariant infrared solution, revealing a potentially novel strong turbulence scaling exponent.
Related
- Vector versus Scalar Beams in Atmospheric Turbulence: Scintillation Index and Average Received Intensity
- Radiation-induced electron spin polarization in ultrarelativistic kinetic turbulence
- Simulation of non-stationary anisotropic capillary wave turbulence within the framework of the kinetic equation
- Thermalization-induced self-polarization of temporally incoherent light: A nonequilibrium wave turbulence kinetic approach
- Conversions between kinetic and surface energy in periodically forced multiphase turbulence
BibTeX
@misc{rosenhaus2026kinetic,
title = {{Kinetic Equations and Turbulence in Large $N$ Vector and SYK-like Models}},
author = {Vladimir Rosenhaus and Daniel Schubring},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19130},
eprint = {2610.19130},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19130},
}
RIS
TY - UNPB
TI - Kinetic Equations and Turbulence in Large N Vector and SYK-like Models
AU - Vladimir Rosenhaus
AU - Daniel Schubring
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.19130
UR - https://arxiv.org/abs/2610.19130
AB - We apply large N expansion techniques to derive kinetic equations for strongly coupled, far-from-equilibrium field theories with O(N) symmetry. For large N vector models, the quasi-classical approximation holds. Incorporating arbitrary momentum-dependent interactions, we show the dynamics obey the standard kinetic equation, with the scattering amplitude given by the retarded propagator of the auxiliary Hubbard-Stratonovich field. This has broad applications to systems like spin wave and Langmuir ion-acoustic turbulence. For large N random coupling (SYK-like) models in d dimensions, leading-order melon diagrams induce order-one propagator renormalization and finite spectral width. The corresponding kinetic equation, unlike those for standard weakly interacting systems, does not have a local-in-time collision integral. We find evidence for a stationary, scale-invariant infrared solution, revealing a potentially novel strong turbulence scaling exponent.
ER -