Volume 79, Number 6, September 2007
Article Number 60003
Number of page(s) 5
Section General
Published online 21 August 2007
EPL, 79 (2007) 60003
DOI: 10.1209/0295-5075/79/60003

Equilibration problem for the generalized Langevin equation

A. Dhar1 and K. Wagh2

1  Raman Research Institute - Bangalore 560080, India
2  Department of Physics and Astronomy, Rutgers University - Piscataway, NJ 08854-8019, USA

received 13 April 2007; accepted in final form 30 July 2007; published September 2007
published online 21 August 2007

We consider the problem of equilibration of a single-oscillator system with dynamics given by the generalized classical Langevin equation. It is well known that this dynamics can be obtained if one considers a model where the single oscillator is coupled to an infinite bath of harmonic oscillators which are initially in equilibrium. Using this equivalence we first determine the conditions necessary for equilibration for the case when the system potential is harmonic. We then give an example with a particular bath where we show that, even for parameter values where the harmonic case always equilibrates, with any finite amount of nonlinearity the system does not equilibrate for arbitrary initial conditions. We understand this as a consequence of the formation of nonlinear localized excitations similar to the discrete breather modes in nonlinear lattices.

05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
05.70.Ln - Nonequilibrium and irreversible thermodynamics.

© Europhysics Letters Association 2007