The equilibrium distribution function for strongly nonlinear systems

TL;DR

This paper develops a new theoretical framework to accurately determine equilibrium distribution functions in strongly nonlinear many-body systems, surpassing traditional methods that fail in such regimes.

Contribution

It introduces a novel approach that incorporates nonlinear effects beyond the random phase approximation, validated across multiple nonlinear models.

Findings

Accurately predicts equilibrium distributions in strongly nonlinear systems

Demonstrates substantial improvements over existing methods

Validates the theory on diverse nonlinear models

Abstract

The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear regimes. We develop a framework to get the equilibrium distributions and dispersion relations in strongly nonlinear many-body systems, incorporating corrections beyond the random phase approximation and capturing intrinsic nonlinear effects. The theory is verified on the nonlinear Schrodinger equation, the Majda-McLaughlin-Tabak model, and the FPUT-beta model, demonstrating its accuracy across distinct types of nonlinear systems. Numerical results show substantial improvements over existing approaches, even in strong nonlinear regimes. This work establishes a theoretical foundation for equilibrium statistical properties in strongly nonlinear systems.