Universal regimes of strong turbulence in the multi-component Gross-Pitaevskii model

TL;DR

This paper develops a comprehensive theory of strong turbulence in the multi-component Gross-Pitaevskii model, revealing universal behaviors in both focusing and defocusing regimes, supported by analytical and numerical evidence.

Contribution

It introduces the first unified theory of strong turbulence for multi-component GP models, highlighting universal regimes independent of interaction strength or pumping level.

Findings

Attractive interactions lead to a critical-balance state unaffected by pumping.

Repulsive interactions exhibit universality, independent of the bare coupling constant.

Analytical results and simulations confirm the proposed turbulence regimes.

Abstract

The Gross-Pitaevskii (GP) model, also known as the nonlinear Schr\"odinger equation, is arguably the most universal model in classical and quantum physics, describing spectrally narrow or long-wavelength distributions of interacting waves or particles. Modern applications -- from oceanic and atmospheric flows to photonics and cold atoms -- predominantly involve states that are far from equilibrium, culminating in the regime of fully developed turbulence. To date, a consistent theoretical description of such states has only existed for weakly interacting quasiparticles. Here we present a theory of strong turbulence in the two-dimensional $N$-component Gross-Pitaevskii model for both repulsive and attractive interactions, corresponding to the defocusing and focusing cases, respectively. In the focusing case, we show that attraction is enhanced by multi-wave effects, leading to a critical-balance state independent of the pumping level. In the defocusing case, repulsion is suppressed by collective effects, giving rise to another type of universality in strong turbulence -- independence from the bare coupling constant. The theory is confirmed by analytical results in the many-component limit and by direct numerical simulations of the single-component GP model.