English

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

Statistical Mechanics 2009-11-11 v3 Soft Condensed Matter

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.

Keywords

Cite

@article{arxiv.cond-mat/0605049,
  title  = {Non-ergodic transitions in many-body Langevin systems: a method of dynamical system reduction},
  author = {Mami Iwata and Shin-ichi Sasa},
  journal= {arXiv preprint arXiv:cond-mat/0605049},
  year   = {2009}
}

Comments

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