Anomalous current fluctuations and mobility-driven clustering

Abstract

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 $\rho =N/L$ 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 ${\rho }_c$. In the steady state, we compute, exactly within a closure scheme, the variance $⟨Q^2(T){⟩}_c=⟨Q^2(T)⟩-⟨Q(T){⟩}^2$ 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 ${\rho }_c$. That is, near criticality, the mobility $\chi (\rho )={\lim }_{L\to \infty }[{\lim }_{T\to \infty }L⟨Q^2(T,L){⟩}_c/2T]\sim (\rho -{\rho }_c{)}^{-1}$ 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 $\rho ={\rho }_c$, the variance has a scaling form $⟨Q^2(T,L){⟩}_c=L^{\gamma }\mathcal{W}(T/L^z)$ with $\gamma =4/3$ 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.

References in corpus (38)

• Motility-Induced Phase Separation
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Macroscopic fluctuation theory
• Macroscopic fluctuation theory for stationary non equilibrium states
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Fluctuations in Stationary non Equilibrium States
• A momentum conserving model with anomalous thermal conductivity in low dimension
• Universal cumulants of the current in diffusive systems on a ring
• Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• Current fluctuations in the zero-range process with open boundaries
• Exact Hydrodynamic Description of Active Lattice Gases
• Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
• DMRG-study of current and activity fluctuations near non-equilibrium phase transitions
• Current fluctuations in non-interacting run-and-tumble particles in one-dimension
• Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
• Phase transition in thermodynamically consistent biochemical oscillators
• Current fluctuations of interacting active Brownian particles
• Equilibrium-like fluctuations in some boundary-driven open diffusive systems
• Generalized Exclusion Processes: Transport Coefficients
• Correlations of the density and of the current in non-equilibrium diffusive systems
• Bose-Einstein Condensation in Scalar Active Matter with Diffusivity Edge
• Current fluctuations in nonequilibrium discontinuous phase transitions
• Current fluctuations in an interacting active lattice gas
• Current fluctuations at a phase transition
• Hydrodynamics, superfluidity and giant number fluctuations in a model of self-propelled particles
• Generalized disorder averages and current fluctuations in run and tumble particles
• Dynamic correlations in the conserved Manna sandpile
• Time-dependent properties of run-and-tumble particles. II.: Current fluctuations
• Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry
• Critical heat current fluctuations in Curie-Weiss model in and out of equilibrium
• Nonequilibrium fluctuations of chemical reaction networks at criticality: The Schlögl model as paradigmatic case
• Reentrant condensation transition in a model of driven scalar active matter with diffusivity edge
• Transport and fluctuations in mass aggregation processes: mobility driven clustering
• Dynamic fluctuations of current and mass in nonequilibrium mass transport processes
• Current fluctuations in the symmetric zero-range process below and at critical density