Hydrodynamics, superfluidity and giant number fluctuations in a model of self-propelled particles

Abstract

We derive hydrodynamics of a prototypical one dimensional model, having variable-range hopping, which mimics passive diffusion and ballistic motion of active, or self-propelled, particles. The model has two main ingredients - the hardcore interaction and the competing mechanisms of short and long range hopping. We calculate two density-dependent transport coefficients - the bulk-diffusion coefficient and the conductivity, the ratio of which, despite violation of detailed balance, is connected to number fluctuation by an Einstein relation. In the limit of infinite range hopping, the model exhibits, upon tuning density $\rho$ (or activity), a "superfluid" transition from a finitely conducting state to an infinitely conducting one, characterized by a divergence in conductivity $\chi (\rho )\sim (\rho -{\rho }_c{)}^{-1}$ with ${\rho }_c$ being the critical density. The diverging conductivity greatly increases particle (or vacancy) mobility and induces "giant" number fluctuations in the system.

arXiv comment19 pages, 4 figures

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• Time-dependent properties of run-and-tumble particles: Density relaxation
• Transport and fluctuations in mass aggregation processes: mobility driven clustering
• Coarsening, condensates and extremes in aggregation-fragmentation models
• Percolation of systems having hyperuniformity or giant number-fluctuations
• Fluctuating Hydrodynamics Describes Transport in Cellular Aggregates
• Density-dependent transport coefficients in two-dimensional cellular aggregates
• A renormalization group study of the dynamics of active membranes: universality classes and scaling laws
• Boundary layers, transport and universal distribution in boundary driven active systems
• Anomalous current fluctuations and mobility-driven clustering