Nonequilibrium inhomogeneous steady state distribution in disordered, mean-field rotator systems

TL;DR

This paper introduces a new method to compute the nonequilibrium steady state distribution in disordered mean-field rotator systems, enabling efficient analysis of complex synchronization phenomena.

Contribution

A novel series expansion method for calculating phase space distributions in disordered mean-field rotator systems, applicable to models like Kuramoto with noise and inertia.

Findings

Method accurately predicts phase space distributions.

Excellent agreement between theory and simulations.

Applicable to models with noise, inertia, and disorder.

Abstract

We present a novel method to compute the phase space distribution in the nonequilibrium stationary state of a wide class of mean-field systems involving rotators subject to quenched disordered external drive and dissipation. The method involves a series expansion of the stationary distribution in inverse of the damping coefficient; the expansion coefficients satisfy recursion relations whose solution requires computing a sparse matrix, making numerical evaluation simple and efficient. We illustrate our method for the paradigmatic Kuramoto model of spontaneous collective synchronization and for its two mode generalization, in presence of noise and inertia, and demonstrate an excellent agreement between simulations and theory for the phase space distribution.