Current browse context:
cond-mat.stat-mech
Change to browse by:
References & Citations
Condensed Matter > Statistical Mechanics
Title: Density relaxation in conserved Manna sandpiles
(Submitted on 2 Nov 2020 (v1), last revised 8 Apr 2021 (this version, v2))
Abstract: We study relaxation of long-wavelength density perturbations in one dimensional conserved Manna sandpile. Far from criticality where correlation length $\xi$ is finite, relaxation of density profiles having wave numbers $k \rightarrow 0$ is diffusive, with relaxation time $\tau_R \sim k^{-2}/D$ with $D$ being the density-dependent bulk-diffusion coefficient. Near criticality with $k \xi \gsim 1$, the bulk diffusivity diverges and the transport becomes anomalous; accordingly, the relaxation time varies as $\tau_R \sim k^{-z}$, with the dynamical exponent $z=2-(1-\beta)/\nu_{\perp} < 2$, where $\beta$ is the critical order-parameter exponent and and $\nu_{\perp}$ is the critical correlation-length exponent. Relaxation of initially localized density profiles on infinite critical background exhibits a self-similar structure. In this case, the asymptotic scaling form of the time-dependent density profile is analytically calculated: we find that, at long times $t$, the width $\sigma$ of the density perturbation grows anomalously, i.e., $\sigma \sim t^{w}$, with the growth exponent $\omega=1/(1+\beta) > 1/2$. In all cases, theoretical predictions are in reasonably good agreement with simulations.
Submission history
From: Dhiraj Tapader [view email][v1] Mon, 2 Nov 2020 18:12:32 GMT (562kb,D)
[v2] Thu, 8 Apr 2021 07:51:08 GMT (558kb,D)
Link back to: arXiv, form interface, contact.