Non-ergodic transitions in many-body Langevin systems: a method of dynamical system reduction

Abstract

We study a non-ergodic transition in a many-body Langevin system. We first derive an equation for the two-point time correlation function of density fluctuations, ignoring the contributions of the third- and fourth-order cumulants. For this equation, with the average density fixed, we find that there is a critical temperature at which the qualitative nature of the trajectories around the trivial solution changes. Using a method of dynamical system reduction around the critical temperature, we simplify the equation for the time correlation function into a two-dimensional ordinary differential equation. Analyzing this differential equation, we demonstrate that a non-ergodic transition occurs at some temperature slightly higher than the critical temperature.

arXiv comment8 pages, 1 figure; ver.3: Calculation errors have been fixed

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Cited by in corpus (3)

• Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation
• A theory for critically divergent fluctuations of dynamical events at non-ergodic transitions
• Scale-free patterns at a saddle-node bifurcation in a stochastic system