We study 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 particle-number fluctuation by an Einstein relation. In the limit of infinite-range hopping, the model exhibits, upon tuning density ρ (or activity), a “superfluid-like” transition from a finitely conducting fluid phase to an infinitely conducting “superfluid” phase, characterized by a divergence in conductivity χ(ρ) ∼ 1/(ρ − ρc ) with ρ_c being the critical density. The diverging conductivity greatly enhances particle mobility and thus induces “giant” number fluctuations in the system.
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Meeting ID: 925 7398 9778