Defects Superdiffusion and Unbinding in a 2D XY Model of Self-Driven Rotors

Abstract

We consider a non-equilibrium extension of the two-dimensional (2D) XY model, equivalent to the noisy Kuramoto model of synchronization with short-range coupling, where rotors sitting on a square lattice are self-driven by random intrinsic frequencies. We study the static and dynamic properties of topological defects (vortices) and establish how self-spinning affects the Berezenskii-Kosterlitz-Thouless phase transition scenario. The non-equilibrium drive breaks the quasi-long-range ordered phase of the 2D XY model into a mosaic of ordered domains of controllable size and results in self-propelled vortices that generically unbind at any temperature, featuring superdiffusion $⟨r^2(t)⟩\sim t^{3/2}$ with a Gaussian distribution of displacements. Our work provides a simple framework to investigate topological defects in active matter and sheds new light on the problem of synchronization of locally coupled oscillators.

arXiv comment6 pages, 5 figures

References in corpus (33)

• Synchronization in complex networks
• The Mechanics and Statistics of Active Matter
• Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas
• Quantised Vortices in an Exciton-Polariton Fluid
• Defect annihilation and proliferation in active nematics
• Orientational order of motile defects in active nematics
• Defect dynamics in active nematics
• Hydrodynamic flow patterns and synchronization of beating cilia
• Velocity Correlations in an Active Nematic
• Generic Conditions for Hydrodynamic Synchronization
• Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects
• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• Data-driven quantitative modeling of bacterial active nematics
• Motility-Induced Microphase and Macrophase Separation in a Two-Dimensional Active Brownian Particle System
• Defect unbinding in active nematics
• Topological order and equilibrium in a condensate of exciton-polaritons
• Non-equilibrium Berezinskii-Kosterlitz-Thouless Transition in a Driven Open Quantum System
• Collective synchronization in spatially extended systems of coupled oscillators with random frequencies
• Entrainment transition in populations of random frequency oscillators
• Quench dynamics of the 2d XY model
• Realizing the physics of motile cilia synchronization with driven colloids
• Hydrodynamics of Active Defects: from order to chaos to defect ordering
• Describing synchronization and topological excitations in arrays of magnetic spin torque oscillators through the Kuramoto model
• Vortex dynamics for two-dimensional XY models
• Defect-Mediated Phase Transitions in Active Soft Matter
• Emergence of dynamic vortex glasses in disordered polar active fluids
• Synchronization in A Carpet of Hydrodynamically Coupled Rotors with Random Intrinsic Frequency
• Quincke oscillations of colloids at planar electrodes
• Vortices and the entrainment transition in the 2D Kuramoto model
• Non-equilibrium Berezinskii-Kosterlitz-Thouless transition in driven-dissipative condensates
• The role of topological defects in the two-stage melting and elastic behavior of active Brownian particles
• Effective equilibrium picture in $xy-$model with exponentially correlated noise
• Abnormal diffusion of a single vortex in the two dimensional XY model

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• 10-GHz-clock time-multiplexed non-degenerate optical parametric oscillator network with a variable planar lightwave circuit interferometer
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