Statistical mechanics of finite arrays of coupled bistable elementsJ. Gómez-Ordóñez1, J. M. Casado1, M. Morillo1, C. Honisch2 and R. Friedrich2
1 Física Teórica, Universidad de Sevilla - Apartado de Correos 1065, Sevilla 41080, Spain, EU
2 Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster - D-48149 Münster, Germany, EU
received 3 July 2009; accepted in final form 30 October 2009; published November 2009
published online 27 November 2009
We discuss the equilibrium of a single collective variable characterizing a finite set of coupled, noisy, bistable systems as the noise strength, the size and the coupling parameter are varied. We identify distinct regions in parameter space. Our finite size results indicate important qualitative differences with respect to those obtained in the asymptotic infinite size limit. We also discuss how to construct approximate 1-dimensional Langevin equations. This equation provides a useful tool to understand the collective behavior even in the presence of an external driving force.
05.45.Xt - Synchronization; coupled oscillators.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
05.40.Ca - Noise.
© EPLA 2009