| Título: | Synchronization for discrete mean-field rotators |
| Autores: |
Jahnel, Benedikt; Ruhr-Universität Bochum Külske, Christof; Ruhr-Universität Bochum |
| Fecha: | 2014-01-02 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Interacting particle systems; non-equilibrium; synchronization; mean-field sytems; discretization; XY model; clock model; rotation dynamics; attractive limit cycle 60K35; 82B26; 82C22 |
| Descripción: | We analyze a non-reversible mean-field jump dynamics for discrete q-valued rotators and show in particular that it exhibits synchronization. The dynamics is the mean-field analogue of the lattice dynamics investigated by the same authors which provides an example of a non-ergodic interacting particle system on the basis of a mechanism suggested by Maes and Shlosman. Based on the correspondence to an underlying model of continuous rotators via a discretization transformation we show the existence of a locally attractive periodic orbit of rotating measures. We also discuss global attractivity, using a free energy as a Lyapunov function and the linearization of the ODE which describes typical behavior of the empirical distribution vector. |
| Idioma: | Inglés |
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