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Superdiffusion, large-scale synchronization, and topological defects

Robert Großmann, Fernando Peruani, and Markus Bär
Phys. Rev. E 93, 040102(R) – Published 8 April 2016
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Abstract

We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby introducing an additional, independent source of fluctuations, thus constituting the intrinsic nonequilibrium nature of the temporal dynamics. We employ this paradigmatic model system to discuss how the emergence of order is affected by the motion of individual entities. In particular, we consider both normal diffusive motion and superdiffusion. A non-Hamiltonian field theory including multiplicative noise terms is derived which describes the nonequilibrium dynamics at the macroscale. This theory reveals a defect-mediated transition from incoherence to quasi-long-range order for normal diffusion of oscillators in two dimensions, implying a power-law dependence of all synchronization properties on system size. In contrast, superdiffusive transport suppresses the emergence of topological defects, thereby inducing a continuous synchronization transition to long-range order in two dimensions. These results are consistent with particle-based simulations.

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  • Received 22 May 2015
  • Revised 8 February 2016

DOI:https://doi.org/10.1103/PhysRevE.93.040102

©2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Robert Großmann1,*, Fernando Peruani2, and Markus Bär1

  • 1Physikalisch-Technische Bundesanstalt Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany
  • 2Laboratoire J. A. Dieudonné, Université de Nice Sophia Antipolis, UMR 7351 CNRS, Parc Valrose, F-06108 Nice Cedex 02, France

  • *grossmann@physik.hu-berlin.de

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Issue

Vol. 93, Iss. 4 — April 2016

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