title: Superdiffusion, large-scale synchronization, and topological defects.
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.
authors.affiliation: Physikalisch-Technische Bundesanstalt Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany.
authors.forename: Robert
authors.initials: R
authors.lastname: Großmann
authors.affiliation: Laboratoire J. A. Dieudonné, Université de Nice Sophia Antipolis, UMR 7351 CNRS, Parc Valrose, F-06108 Nice Cedex 02, France.
authors.forename: Fernando
authors.initials: F
authors.lastname: Peruani
authors.affiliation: Physikalisch-Technische Bundesanstalt Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany.
authors.forename: Markus
authors.initials: M
authors.lastname: Bär