Equilibration problem for the generalized Langevin equation

Details Equilibration problem for the generalized Langevin equation Equilibration problem for the generalized Langevin equation

2006-04-06

arxiv.org/abs/cond-mat/0604170v2

Europhys. Lett. 79, 60003 (2007)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 2 figures

Scientific paper

10.1209/0295-5075/79/60003

We consider the problem of equilibration of a single oscillator system with dynamics given by the generalized 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.

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