arXiv subjects

Punyabrata Pradhan

Publications and source records attributed to Punyabrata Pradhan.

At least 19 recordsLinked to original sources

arXiv2026

Odd diffusion and power-law correlations in chiral mass-transport processes

We study mass-conserving Markov jump processes on a square lattice, where masses hop with a preferred rotational sense, thus breaking both time-reversal and mirror symmetries. We consider closed systems with both periodic and open (reflecting) boundaries, the latter supporting a steady-state edge current. We show that odd diffusion, arising from the chiral transport, generically provides a mechanism for the emergence of scale-invariant two-point density correlations in nonequilibrium steady states even in the presence of lattice rotation symmetry -- a mechanism that is qualitatively distinct from the well-known mechanism of anisotropic hopping. We exactly calculate the steady-state equal-time density-density correlations, which exhibit an algebraic decay, $C(\mathbf{r}) \sim |\mathbf{r}|^{-4}$ for $|\mathbf{r}| \gg 1$. This algebraic behavior results from the interplay between the off-diagonal components of the diffusion and mobility tensors, demonstrating that chiral transport alone can generate power-law correlations in isotropic driven systems. Remarkably, the structure factor in the zero-wavenumber limit and the amplitude of the power laws depend nontrivially on chirality. While increasing chirality initially suppresses large-scale density fluctuations, the fluctuations beyond a threshold odd-diffusion strength vary nonmonotonically with chirality and develop a cusp singularity.

cond-mat.stat-mech↗

arXiv2026

Power laws, anisotropy and center-of-mass conservation in mass transport processes

We present exact results for steady-state density correlation functions in conserved-mass transport processes with {\it anisotropic}, reflection-symmetric hopping on a $d-$dimensional hypercubic lattice. In addition to mass conservation, we consider center-of-mass (CoM) conservation, imposed either along a specific axis or along all axes. CoM-conserving dynamics is implemented through coordinated {\it multidirectional} hopping of two equal chunks of masses in {\it opposite} directions. While anisotropy and mass conservation are known to generate power-law density correlations $C({\bf x}) \sim 1/|{\bf x}|^d$ at large distance $|{\bf x}| \gg 1$ {\it [Phys. Rev. A {\bf 42}, 1954 (1990)]}, an additional CoM conservation can qualitatively alter the nature of the power law. Indeed, when CoM is conserved in {\it all} directions, the correlations decay faster $-$ typically as $C({\bf x}) \sim 1/|{\bf x}|^{(d+2)}$, regardless of the presence (or absence) of anisotropy. Consequently, the systems exhibit an extreme {\it hyperuniformity} (``class I''), where the long-wavelength density fluctuations, despite the slow power-law decay, are anomalously suppressed. When CoM is conserved along particular ({\it not} all) directions, the slower $1/|{\bf x}|^{d}$ power-law decay is recovered. The above behavior can be understood from an analogy between the correlation function and an electrostatic potential: While a (rank-$2$) quadrupolar charge distribution gives rise to the $1/|{\bf x}|^{d}$ power law, the $1/|{\bf x}|^{(d+2)}$ power law originates from a higher-order (rank-$4$) multipolar charge distribution. These findings reveal a rich interplay between anisotropy and CoM conservation in nonequilibrium steady states.

cond-mat.stat-mech↗

arXiv2025

Generic power laws in higher-dimensional lattice models with multidirectional hopping

We show that, on a $d-$dimensional hypercubic lattice with $d>1$, conserved-mass transport processes, with {\it multidirectional} hopping that respect all symmetries of the lattice, exhibit power-law correlations for generic parameter values $-$ even {\it far} from phase transition point, if any. The key idea for generating the algebraic decay is the notion of {\it multidirectional} hopping, which means that several chunks of masses, or several particles, can hop out simultaneously from a lattice site in multiple directions, consequently breaking detailed balance. Notably, the systems we consider are described by a continuous-time Markov process, are diffusive, {\it lattice-rotation symmetric}, spatially homogeneous and thus have {\it no} net mass current. Using hydrodynamic and exact microscopic theory, we show that, for spatial dimensions $d > 1$, the steady-state static density-density and ``activity''-density correlation functions in the thermodynamic limit typically decay as $\sim 1/r^{(d+2)}$ at large distance $r=|{\bf r}|$; the strength of the power law is exactly calculated for several models and expressed in terms of the density-dependent bulk-diffusion coefficient and Onsager matrix (or, mobility tensor). In particular, our theory explains why center-of-mass-conserving dynamics, used to model novel disordered {\it hyperuniform} state of matter, result in generic long-ranged correlations. However, in a restricted parameter regime, the correlations can also be short ranged and are characterized through the Onsager matrix.

cond-mat.stat-mech↗

arXiv2025

Anomalous current fluctuations and mobility-driven clustering

We study steady-state current fluctuations in hardcore lattice gases on a ring of $L$ sites, where $N$ particles perform symmetric, {\it extended-ranged} hopping. The hop length is a random variable depending on a length scale $l_0$ (hopping range) and the inter-particle gap. The systems have mass-conserving dynamics with global density $ρ= N/L$ fixed, but violate detailed balance. We consider two analytically tractable cases: (i) $l_0 = 2$ (finite-ranged) and (ii) $l_0 \to \infty$ (infinite-ranged); in the latter, the system undergoes a clustering or condensation transition below a critical density $ρ_c$. In the steady state, we compute, exactly within a closure scheme, the variance $\langle Q^2(T) \rangle_c = \langle Q^2(T) \rangle - \langle Q(T) \rangle^2$ of the cumulative (time-integrated) current $Q(T)$ across a bond $(i,i+1)$ over a time interval $[0, T]$. We show that for $l_0 \to \infty$, the scaled variance of the time-integrated bond current, or equivalently, the mobility diverges at $ρ_c$. That is, near criticality, the mobility $χ(ρ) = \lim_{L \to \infty} [\lim_{T \to \infty} L \langle Q^2(T, L) \rangle_c / 2T] \sim (ρ- ρ_c)^{-1}$ has a simple-pole singularity, thus providing a dynamical characterization of the condensation transition, previously observed in a related mass aggregation model by Majumdar et al.\ [{\it Phys.\ Rev.\ Lett.\ {\bf 81}, 3691 (1998)}]. At the critical point $ρ= ρ_c$, the variance has a scaling form $\langle Q^2(T, L) \rangle_c = L^γ {\cal W}(T/L^{z})$ with $γ= 4/3$ and the dynamical exponent $z = 2$. Thus, near criticality, the mobility {\it diverges} while the diffusion coefficient remains {\it finite}, {\it unlike} in equilibrium systems with short-ranged hopping, where diffusion coefficient usually {\it vanishes} and mobility remains finite.

cond-mat.stat-mech↗

arXiv2025

Hyperuniformity in mass transport processes with center-of-mass conservation: Some exact results

We characterize steady-state static and dynamic properties in a broad class of mass transport processes on a periodic hypercubic lattice of volume $L^d$, where both mass and {\it center-of-mass} (CoM) remain conserved and detailed balance is violated in the bulk; we specifically consider these models in $d=1$ and $2$ dimensions. Using a microscopic approach, we exactly determine the decay (or, growth) exponents for various dynamic and static correlation functions. We show that, despite constrained dynamics due to the CoM conservation (CoMC), the density relaxation is indeed diffusive. However, fluctuation properties are strikingly different from that in the diffusive systems with a single (mass) conservation law. In the thermodynamic limit, the steady-state variance $\langle {\cal Q}^2(T) \rangle_c$ of time-integrated bond current ${\cal Q}(T)$ across a bond in time interval $T$ exhibits the following long-time behavior: $\langle {\cal Q}^2(T) \rangle_c \simeq A_1 T + A_2 + A_3 T^{-d/2}$. Remarkably, depending on dimensions and microscopic details, the prefactor $A_1$ can vanish (e.g., for $d=1$), causing the variance to eventually {\it saturate}. The exponents governing the small-frequency behavior of the power spectrum $S_J(f) \sim f^{ψ_J}$ for bond current are exactly determined as $ψ_J=3/2$ and $2$ in $d=1$ and $2$ dimensions, respectively, implying a ``dynamic hyperuniformity''. We also compute the static structure factor $S(q)$, which, in the small-$q$ limit, varies as the square of wave number $q$, i.e., $S(q) \sim q^2$. Indeed, both dynamic and static fluctuations are anomalously suppressed, resulting in an extreme form of (``class I'') hyperuniformity in the systems.

cond-mat.stat-mech↗

arXiv2024

Current fluctuations in the symmetric zero-range process below and at critical density

Characterizing current fluctuations in a steady state is of fundamental interest and has attracted considerable attention in the recent past. However, the bulk of the studies are limited to systems that either do not exhibit a phase transition or are far from criticality. Here we consider a symmetric zero-range process on a ring that is known to show a phase transition in the steady state. We analytically calculate two density-dependent transport coefficients, namely, the bulk-diffusion coefficient and the particle mobility, that characterize the first two cumulants of the time-integrated current. We show that on the hydrodynamic scale, away from the critical point, the variance of the time-integrated current in the steady state grows with time $t$ as $\sqrt{t}$ and $t$ at short and long times, respectively. Moreover, we find an expression of the full scaling function for the variance of the time-integrated current and thereby the amplitude of the temporal growth of the current fluctuations. At the critical point, using a scaling theory, we find that, while the above-mentioned long-time scaling of the variance of the cumulative current continues to hold, the short-time behavior is anomalous in that the growth exponent is larger than one-half and varies continuously with the model parameters.

cond-mat.stat-mech↗

arXiv2024

Dynamic fluctuations of current and mass in nonequilibrium mass transport processes

We study steady-state dynamic fluctuations of current and mass, as well as the corresponding power spectra, in conserved-mass transport processes on a ring of $L$ sites; these processes violate detailed balance, have nontrivial spatial structures, and their steady states are not described by the Boltzmann-Gibbs distribution. We exactly calculate, for all times $T$, the fluctuations $\langle \mathcal{Q}_i^2(T) \rangle$ and $\langle \mathcal{Q}_{sub}^2(l, T) \rangle$ of the cumulative currents upto time $T$ across $i$th bond and across a subsystem of size $l$ (summed over bonds in the subsystem), respectively; we also calculate the (two-point) dynamic correlation function for subsystem mass. In particular, we show that, for large $L \gg 1$, the bond-current fluctuation grows linearly for $T \sim {\cal O}(1)$, subdiffusively for $T \ll L^2$ and then again linearly for $T \gg L^2$. The scaled subsystem current fluctuation $\lim_{l \rightarrow \infty, T \rightarrow \infty} \langle \mathcal{Q}^2_{sub}(l, T) \rangle/2lT$ converges to the density-dependent particle mobility $χ$ when the large subsystem size limit is taken first, followed by the large time limit. Remarkably, the scaled current fluctuation $D \langle \mathcal{Q}_i^2(T)\rangle/2 χL \equiv {\cal W}(y)$ as a function of scaled time $y=DT/L^2$ is expressed in terms of a universal scaling function ${\cal W}(y)$, where $D$ is the bulk-diffusion coefficient. Similarly, the power spectra for current and mass time series are characterized by the respective universal scaling functions, which are calculated exactly. We provide a microscopic derivation of equilibrium-like Green-Kubo and Einstein relations, that connect the steady-state current fluctuations to the response to an external force and to mass fluctuation, respectively.

cond-mat.stat-mech↗

arXiv2024

Time-dependent properties of run-and-tumble particles: Density relaxation

We characterize collective diffusion of hardcore run-and-tumble particles (RTPs) by explicitly calculating the bulk-diffusion coefficient $D(ρ, γ)$ in two minimal models on a $d$ dimensional periodic lattice for arbitrary density $ρ$ and tumbling rate $γ$. We focus on two models: Model I is the standard version of hardcore RTPs [Phys. Rev. E \textbf{89}, 012706 (2014)], whereas model II is a long-ranged lattice gas (LLG) with hardcore exclusion - an analytically tractable variant of model I; notably, both models are found to have qualitatively similar features. In the strong-persistence limit $γ\rightarrow 0$ (i.e., dimensionless $r_0 γ/v \rightarrow 0$), with $v$ and $r_{0}$ being the self-propulsion speed and particle diameter, respectively, the fascinating interplay between persistence and interaction is quantified in terms of two length scales - mean gap, or "mean free path", and persistence length $l_{p}=v/ γ$. Indeed, for a small tumbling rate, the bulk-diffusion coefficient varies as a power law in a wide range of density: $D \propto ρ^{-α}$, with exponent $α$ gradually crossing over from $α= 2$ at high densities to $α= 0$ at low densities. Thus, the density relaxation is governed by a nonlinear diffusion equation with anomalous spatiotemporal scaling. Moreover, in the thermodynamic limit, we show that the bulk-diffusion coefficient - for $ρ,γ\rightarrow 0$ with $ρ/γ$ fixed - has a scaling form $D(ρ, γ) = D^{(0)}\mathcal{F}(ψ=ρa v/γ)$, where $a\sim r_{0}^{d-1}$ is particle cross-section and $D^{(0)}$ is proportional to the diffusivity of noninteracting particles; the scaling function $\mathcal{F}(ψ)$ is calculated analytically for model I and numerically for model II. Our arguments are independent of dimensions and microscopic details.

cond-mat.stat-mech↗

arXiv2024

Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry

We study a paradigmatic model of absorbing-phase transition - the Oslo model - on a one-dimensional ring of $L$ sites with a fixed global density $\barρ$; notably, microscopic dynamics conserve both mass and \textit{center of mass (CoM), but lacks time-reversal symmetry}. Despite having highly constrained dynamics due to CoM conservation, the system exhibits diffusive relaxation away from criticality and superdiffusive relaxation near criticality. Furthermore, the CoM conservation severely restricts particle movement, rendering the mobility to vanish exactly. Indeed the temporal growth of current fluctuation is qualitatively different from that observed in diffusive systems with a single conservation law. Away from criticality, steady-state fluctuation $\langle \mathcal{Q}_i^2(T,Δ) \rangle$ of current $\mathcal{Q}_i$ across $i$th bond up to time $T$ \textit{saturates} as $\langle \mathcal{Q}_i^2 \rangle \simeq Σ_Q^2(Δ) - {\rm const.} T^{-1/2}$; near criticality, it grows subdiffusively as $\langle \mathcal{Q}_i^2 \rangle \sim T^α$, with $0 < α< 1/2$, and eventually \textit{saturates} to $Σ_Q^2(Δ)$. The asymptotic current fluctuation $Σ_Q^2(Δ)$ is a \textit{nonmonotonic} function of $Δ$: It diverges as $Σ_Q^2(Δ) \sim Δ^2$ for $Δ\gg ρ_c$ and $Σ_Q^2(Δ) \sim Δ^{-δ}$, with $δ> 0$, for $Δ\to 0^+$. By using a mass-conservation principle, we exactly determine the exponents $δ= 2(1-1/ν_\perp)/ν_\perp$ and $α= δ/z ν_\perp$ via the correlation-length and dynamic exponents, $ν_\perp$ and $z$, respectively. Finally, we show that, in the steady state, the self-diffusion coefficient $\mathcal{D}_s(\barρ)$ of tagged particles is connected to activity by $\mathcal{D}_s(\barρ) = a(\barρ) / \barρ$.

cond-mat.stat-mech↗

arXiv2023

Time-dependent properties of run-and-tumble particles. II.: Current fluctuations

We investigate steady-state current fluctuations in two models of run-and-tumble particles (RTPs) on a ring of $L$ sites, for \textit{arbitrary} tumbling rate $γ=τ_p^{-1}$ and density $ρ$; model I consists of standard hardcore RTPs, while model II is an analytically tractable variant of model I, called long-ranged lattice gas (LLG). We show that, in the limit of $L$ large, the fluctuation of cumulative current $Q_i(T, L)$ across $i$th bond in a time interval $T \gg 1/D$ grows first {\it subdiffusively} and then {\it diffusively} (linearly) with $T$, where $D$ is the bulk diffusion coefficient. Remarkably, regardless of the model details, the scaled bond-current fluctuations $D \langle Q_i^2(T, L) \rangle/2 χL \equiv {\cal W}(y)$ as a function of scaled variable $y=DT/L^2$ collapse onto a {\it universal} scaling curve ${\cal W}(y)$, where $χ(ρ,γ)$ is the collective particle {\it mobility}. In the limit of small density and tumbling rate $ρ, γ\rightarrow 0$ with $ψ=ρ/γ$ fixed, there exists a scaling law: The scaled mobility $γ^{a} χ(ρ, γ)/χ^{(0)} \equiv {\cal H} (ψ)$ as a function of $ψ$ collapse onto a scaling curve ${\cal H}(ψ)$, where $a=1$ and $2$ in models I and II, respectively, and $χ^{(0)}$ is the mobility in the limiting case of symmetric simple exclusion process (SSEP). For model II (LLG), we calculate exactly, within a truncation scheme, both the scaling functions, ${\cal W}(y)$ and ${\cal H}(ψ)$. We also calculate spatial correlation functions for the current, and compare our theory with simulation results of model I; for both models, the correlation functions decay exponentially, with correlation length $ξ\sim τ_p^{1/2}$ diverging with persistence time $τ_p \gg 1$. Overall our theory is in excellent agreement with simulations and complements the findings of Ref. {\it arXiv:2209.11995}.

cond-mat.stat-mech↗

arXiv2023

Dynamic correlations in the conserved Manna sandpile

We study dynamic correlations for current and mass, as well as the associated power spectra, in the one-dimensional conserved Manna sandpile. We show that, in the thermodynamic limit, the variance of cumulative bond current up to time $T$ grows subdiffusively as $T^{1/2-μ}$ with the exponent $μ\ge 0$ depending on the density regimes considered and, likewise, the power spectra of current and mass at low frequency $f$ varies as $f^{1/2+μ}$ and $f^{-3/2+μ}$, respectively; our theory predicts that, far from criticality, $μ= 0$ and, near criticality, $μ= (β+1)/2 ν_{\perp} z > 0$ with $β$, $ν_{\perp}$ and $z$ being the order-parameter, correlation-length and dynamic exponents, respectively. The anomalous suppression of fluctuations near criticality signifies a "dynamic hyperuniformity", characterized by a set of fluctuation relations, in which current, mass and tagged-particle displacement fluctuations are shown to have a precise quantitative relationship with the density-dependent activity (or, it's derivative). In particular, the relation, ${\mathcal{D}}_s(\barρ) = a(\barρ) / \barρ$, between the self-diffusion coefficient ${\mathcal{D}}_s(\barρ)$, activity $a(\barρ)$ and density $\barρ$ explains a previous simulation observation [Eur. Phys. J. B \textbf{72}, 441 (2009)] that, near criticality, the self-diffusion coefficient in the Manna sandpile has the same scaling behavior as the activity.

cond-mat.stat-mech↗

arXiv2023

Optimum transport in systems with time-dependent drive and short-ranged interactions

We study one-dimensional hardcore lattice gases, with nearest-neighbor interactions, in the presence of an external potential barrier, that moves on the periodic lattice with a constant speed. We investigate how the nature of the interaction (attractive or repulsive) affects particle transport and determine, using numerical simulations and mean-field calculations, the conditions for an optimum transport in the system. Physically, the particle current induced by the time-dependent potential is opposed by a diffusive current generated by the density inhomogeneity (a traveling wave) built up in the system, resulting in a current reversal, that crucially depends on the speed of the barrier and particle-number density. Indeed the presence of nearest-neighbor interaction has a significant impact on the current: Repulsive interaction enhances the current, whereas attractive interaction suppresses it considerably. Quite remarkably, when the number density is low, the current increases with the strength of the repulsive interaction and the maximum current is obtained for the strongest possible repulsion strength, i.e., for the nearest-neighbor exclusion. However, at high density, very strong repulsion makes particle movement difficult in an overcrowded environment and, in that case, the maximal current is achieved for weaker repulsive interaction strength.

cond-mat.stat-mech↗

arXiv2021

Transport and fluctuations in mass aggregation processes: mobility driven clustering

We calculate the bulk-diffusion coefficient and the conductivity in a broad class of conserved-mass aggregation processes on a ring of discrete sites. These processes involve chipping and fragmentation of masses, which diffuse around and aggregate upon contact with their neighboring masses. We find that, even in the absence of microscopic time reversibility, the systems satisfy an Einstein relation, which connects the ratio of the conductivity and the bulk-diffusion coefficient to mass fluctuation. Interestingly, when aggregation dominates over chipping, the conductivity or, equivalently, the mobility, gets enhanced. The enhancement in conductivity, in accordance with the Einstein relation, results in large mass fluctuations, implying a {\it mobility driven clustering} in the system. Indeed, in a certain parameter regime, we demonstrate that the conductivity diverges beyond a critical density, signaling the onset of a condensation transition observed in the past. In a striking similarity to Bose-Einstein condensation, the condensate formation along with the diverging conductivity thus underlies a dynamic "superfluidlike" transition in these nonequilibrium systems. Notably, the bulk-diffusion coefficient remains finite in all cases. Our analytic results are in a quite good agreement with simulations.

cond-mat.stat-mech↗

arXiv2021

Density relaxation in conserved Manna sandpiles

We study relaxation of long-wavelength density perturbations in one dimensional conserved Manna sandpile. Far from criticality where correlation length $ξ$ is finite, relaxation of density profiles having wave numbers $k \rightarrow 0$ is diffusive, with relaxation time $τ_R \sim k^{-2}/D$ with $D$ being the density-dependent bulk-diffusion coefficient. Near criticality with $k ξ\gsim 1$, the bulk diffusivity diverges and the transport becomes anomalous; accordingly, the relaxation time varies as $τ_R \sim k^{-z}$, with the dynamical exponent $z=2-(1-β)/ν_{\perp} < 2$, where $β$ is the critical order-parameter exponent and and $ν_{\perp}$ 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 $σ$ of the density perturbation grows anomalously, i.e., $σ\sim t^{w}$, with the growth exponent $ω=1/(1+β) > 1/2$. In all cases, theoretical predictions are in reasonably good agreement with simulations.

cond-mat.stat-mech↗

arXiv2020

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

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 $ρ$ (or activity), a "superfluid" transition from a finitely conducting state to an infinitely conducting one, characterized by a divergence in conductivity $χ(ρ) \sim (ρ-ρ_c)^{-1}$ with $ρ_c$ being the critical density. The diverging conductivity greatly increases particle (or vacancy) mobility and induces "giant" number fluctuations in the system.

cond-mat.stat-mech↗

arXiv2019

Additivity and density fluctuations in Vicsek-like models of self-propelled particles

We study coarse-grained density fluctuations in the disordered phase of the paradigmatic Vicsek-like models of self-propelled particles with alignment interactions and random self-propulsion velocities. By numerically integrating a fluctuation-response relation - the direct consequence of an additivity property, we compute logarithm of the large-deviation probabilities of the coarse-grained subsystem density, while the system is in the disordered fluid phase with vanishing macroscopic velocity. The large-deviation probabilities, computed within additivity, agree remarkably well with that obtained from direct microscopic simulations of the models. Our results provide an evidence of the existence of an equilibrium-like chemical potential, which governs the coarse-grained density fluctuations in the Vicsek-like models. Moreover, comparison of the particle-number fluctuations among several self-propelled particle systems suggests a common mechanism through which the number fluctuations arise in such systems.

cond-mat.stat-mech↗

arXiv2018

Current reversal in interacting colloids under time-periodic drive

Using molecular dynamics simulations, we study particle-transport in a system of interacting colloidal particles on a ring, where the system is driven by a time-dependent external potential, moving along the ring. We consider two driving protocols: (i) the external potential barrier moves with a uniform velocity $v$ along the ring, and (ii) it moves in discrete jumps with jump-length $l$ and waiting time $τ$ with an effective velocity $v=l/τ$. The time-averaged (dc) particle current, which always remains positive in case (i), interestingly reverses its direction in case (ii) upon tuning the particle-number density $ρ_0$ and the effective barrier velocity $v$. We also find a scaling form for the current in terms of number density, barrier velocity, barrier height and temperature of the system.

cond-mat.stat-mech↗

arXiv2018

Hydrodynamics, density fluctuations and universality in conserved stochastic sandpiles

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 equilibriumlike chemical potential $μ(ρ) \sim \ln a(ρ)$ where $a(ρ)$ is the activity in the system. Using the above hydrodynamics, we derive two scaling relations: As $Δ= (ρ- ρ_c) \rightarrow 0^+$, $ρ_c$ being the critical density, (i) the mass-fluctuation $σ^2(ρ) \sim Δ^{1-δ}$ with $δ=0$ and (ii) the dynamical exponent $z = 2 + (β-1)/ν_{\perp}$, expressed in terms of two static exponents $β$ and $ν_{\perp}$ for activity $a(ρ) \sim Δ^β$ and correlation length $ξ\sim Δ^{-ν_{\perp}}$, respectively. Our results imply that conserved Manna sandpile, a well studied variant of the CSS, belongs to a distinct universality - {\it not} that of directed percolation (DP), which, without any conservation law as such, does not obey scaling relation (ii).

cond-mat.stat-mech↗