The partially asymmetric zero range process with quenched disorder

Abstract

We consider the one-dimensional partially asymmetric zero range process where the hopping rates as well as the easy direction of hopping are random variables. For this type of disorder there is a condensation phenomena in the thermodynamic limit: the particles typically occupy one single site and the fraction of particles outside the condensate is vanishing. We use extreme value statistics and an asymptotically exact strong disorder renormalization group method to explore the properties of the steady state. In a finite system of $L$ sites the current vanishes as $J\sim L^{-z}$, where the dynamical exponent, $z$, is exactly calculated. For $0<z<1$ the transport is realized by $N_a\sim L^{1-z}$ active particles, which move with a constant velocity, whereas for $z>1$ the transport is due to the anomalous diffusion of a single Brownian particle. Inactive particles are localized at a second special site and their number in rare realizations is macroscopic. The average density profile of inactive particles has a width of, $\xi \sim {\delta }^{-2}$, in terms of the asymmetry parameter, $\delta$. In addition to this, we have investigated the approach to the steady state of the system through a coarsening process and found that the size of the condensate grows as $n_L\sim t^{1/(1+z)}$ for large times. For the unbiased model $z$ is formally infinite and the coarsening is logarithmically slow.

12 pages, 9 figures

References in corpus (28)

• Statistical Physics of Vehicular Traffic and Some Related Systems
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Connectivity of Growing Random Networks
• Bose-Einstein condensation in complex networks
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Strong disorder RG approach of random systems
• Bose-Einstein Condensation In Disordered Exclusion Models and Relation to Traffic Flow
• Kinetics of Clustering in Traffic Flows
• Random Walkers in 1-D Random Environments: Exact Renormalization Group Analysis
• Sand as Maxwell's demon
• Condensation in the zero range process: stationary and dynamical properties
• Criterion for phase separation in one-dimensional driven systems
• Strong disorder fixed point in absorbing state phase transitions
• Exact Results for the Asymmetric Simple Exclusion Process with a Blockage
• Phase separation in disordered exclusion models
• Driven Lattice Gases with Quenched Disorder: Exact Results and Different Macroscopic Regimes
• Absorbing state phase transitions with quenched disorder
• Steady State and Dynamics of Driven Diffusive Systems with Quenched Disorder
• Dynamics of Molecular Motors and Polymer Translocation with Sequence Heterogeneity
• The Random Transverse Ising Spin Chain and Random Walks
• Disordered asymmetric simple exclusion process: mean-field treatment
• Partially asymmetric exclusion models with quenched disorder
• Exact renormalization of the random transverse-field Ising spin chain in the strongly ordered and strongly disordered Griffiths phases
• Sample-Dependent Phase Transitions in Disordered Exclusion Models
• Dynamics of a disordered, driven zero range process in one dimension
• Localization properties of the anomalous diffusion phase $x{t}^{\mu }$ in the directed trap model and in the Sinai diffusion with bias
• Dynamics of Molecular Motors with Finite Processivity on Heterogeneous Tracks
• Anomalous coarsening and glassy dynamics

Cited by in corpus (23)

• Renormalization group study of the two-dimensional random transverse-field Ising model
• On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
• Driven Diffusive Systems with Disorder
• Partially Asymmetric Exclusion Processes with Sitewise Disorder
• Single-Bottleneck Approximation for Driven Lattice Gases with Disorder and Open Boundary Conditions
• Condensation in the inhomogeneous zero-range process: an interplay between interaction and diffusion disorder
• Strong Griffiths singularities in random systems and their relation to extreme value statistics
• Random walks and polymers in the presence of quenched disorder
• Non equilibrium dynamics of disordered systems : understanding the broad continuum of relevant time scales via a strong-disorder RG in configuration space
• Random elastic networks : strong disorder renormalization approach
• Equilibrium of disordered systems : constructing the appropriate valleys in each sample via strong disorder renormalization in configuration space
• Competition between quenched disorder and long-range connections: A numerical study of diffusion
• Random walk in two-dimensional self-affine random potentials : strong disorder renormalization approach
• Non-equilibrium dynamics of finite-dimensional disordered systems : RG flow towards an "infinite disorder" fixed point at large times
• Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?
• Random walks in a random environment on a strip: a renormalization group approach
• Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
• Anomalous transport in disordered exclusion processes with coupled particles
• Distribution of dynamical quantities in the contact process, random walks, and quantum spin chains in random environments
• Anomalous diffusion in disordered multi-channel systems
• Unusual features of coarsening with detachment rates decreasing with cluster mass
• Renormalization-group investigation of the S=1 random antiferromagnetic Heisenberg Chain
• Condensate formation in a zero-range process with random site capacities