Nonequilibrium dynamics of the zeta urn model
Service de Physique de l'État Condensé, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
2 Service de Physique Théorique (URA 2306 of CNRS) , CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
Published online: 15 October 2001
We consider a mean-field dynamical urn model, defined by rules which give the rate at which a ball is drawn from an urn and put in another one, chosen amongst an assembly. At equilibrium, this model possesses a fluid and a condensed phase, separated by a critical line. We present an analytical study of the nonequilibrium properties of the fluctuating number of balls in a given urn, considering successively the temporal evolution of its distribution, of its two-time correlation and response functions, and of the associated fluctuation-dissipation ratio, both along the critical line and in the condensed phase. For well separated times the fluctuation-dissipation ratio admits non-trivial limit values, both at criticality and in the condensed phase, which are universal quantities depending continuously on temperature.
PACS: 02.50.Ey – Stochastic processes / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 61.43.Fs – Glasses
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001