Hydrodynamics, density fluctuations, and universality in conserved stochastic sandpiles.
Phys Rev E
; 97(6-1): 062142, 2018 Jun.
Article
em En
| MEDLINE
| ID: mdl-30011450
ABSTRACT
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)â¼lna(ρ), where a(ρ) is the activity in the system. By using the above hydrodynamics, we derive two scaling relations As Δ=(ρ-ρ_{c})â0^{+}, ρ_{c} being the critical density, (i) the mass fluctuation σ^{2}(ρ)â¼Δ^{1-δ} with δ=0 and (ii) the dynamical exponent z=2+(ß-1)/ν_{â¥}, expressed in terms of two static exponents ß and ν_{â¥} for activity a(ρ)â¼Δ^{ß} and correlation length ξâ¼Δ^{-ν_{â¥}}, 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).
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Ano de publicação:
2018
Tipo de documento:
Article