Article

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

05/2006; DOI:doi:10.1088/1742-5468/2006/10/L10003
Source: arXiv

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

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### Keywords

1 figure

8 pages

Calculation errors

contributions

critical temperature

differential equation

dynamical system reduction

many-body Langevin system

time correlation function

trajectories

two-dimensional ordinary differential equation

two-point time correlation function