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Synchronization for discrete mean-field rotators


 
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1. Title Title of document Synchronization for discrete mean-field rotators
 
2. Creator Author's name, affiliation, country Benedikt Jahnel; Ruhr-Universität Bochum; Germany
 
2. Creator Author's name, affiliation, country Christof Külske; Ruhr-Universität Bochum; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Interacting particle systems; non-equilibrium; synchronization; mean-field sytems; discretization; XY model; clock model; rotation dynamics; attractive limit cycle
 
3. Subject Subject classification 60K35; 82B26; 82C22
 
4. Description Abstract

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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) SFB/TR 12, DFG
 
7. Date (YYYY-MM-DD) 2014-01-20
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2948
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-2948
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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