Hydrodynamics, density fluctuations, and universality in conserved stochastic sandpiles

摘要

We study conserved stochastic sandpiles (CSSs), which exhibit an active-absorbing phase transition upon tuning density ρ. We demonstrate that a broad class of CSSs possesses a remarkable hydrodynamic structure: There is an Einstein relation σ~2(ρ) = χ(ρ)/D(ρ), which connects bulk-diffusion coefficient D(ρ), conductivity χ(ρ), and mass fluctuation, or scaled variance of subsystem mass, σ~2(ρ). Consequently, density large-deviations are governed by an equilibrium-like chemical potential μ(ρ) ～ ln a(ρ), where a(ρ) is the activity in the system. By using the above hydrodynamics, we derive two scaling relations: As? = (ρ ? ρc) → 0~+, ρ_c being the critical density, (i) the mass fluctuation σ~2(ρ) ～ ?~(1?δ) with δ = 0 and (ii) the dynamical exponent z = 2 + (β ? 1)/ν_⊥, expressed in terms of two static exponents β and ν_⊥ for activity a(ρ) ～ ?~β and correlation length ξ ～ ?~(?ν⊥) , respectively. Our results imply that conserved Manna sandpile, a well studied variant of the CSS, belongs to a distinct universality—not that of directed percolation (DP), which, without any conservation law as such, does not obey scaling relation (ii).