Phase transitions in an exactly soluble one-dimensional exclusion process

Abstract

We consider an exclusion process, with particles injected with rate $\alpha$ at the origin and removed with rate $\beta$ at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop onto unoccupied sites, to the right only. For the special case of $\alpha =\beta =1$ the model was solved previously by Derrida et al. Here we extend the solution to general $\alpha ,\beta$. The phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation.

LATEX (23 pages, one figure only partially included, complete figure available upon request), Weizmann preprint WIS-92/96/Dec.-PH

References in corpus (1)

• Time-dependent correlation functions in a one-dimensional asymmetric exclusion process

Cited by in corpus (311)

• Traffic and Related Self-Driven Many-Particle Systems
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Discrete stochastic models for traffic flow
• Phase Coexistence in Driven One Dimensional Transport
• Particle hopping models and traffic flow theory
• The totally asymmetric exclusion process with extended objects, a model for protein synthesis
• Physics of Transport and Traffic Phenomena in Biology: from molecular motors and cells to organisms
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Nonequilibrium Physics in Biology
• Exact Solution of the Master Equation for the Asymmetric Exclusion Process
• Clustered bottlenecks in mRNA translation and protein synthesis
• Traffic of molecular motors through tube-like compartments
• Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments
• Steady-state selection in driven diffusive systems with open boundaries
• Shock formation in an exclusion process with creation and annihilation
• Bose-Einstein Condensation In Disordered Exclusion Models and Relation to Traffic Flow
• Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
• Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries
• Reconstruction on trees and spin glass transition
• Partially Asymmetric Exclusion Process with Open Boundaries
• Exact solution of a cellular automaton for traffic
• Localization of shocks in driven diffusive systems without particle number conservation
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Theoretical vs. Empirical Classification and Prediction of Congested Traffic States
• Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra
• Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
• Asymmetric Simple Exclusion Process with Open Boundaries and Askey-Wilson Polynomials
• Exact Current Statistics of the ASEP with Open Boundaries
• Exact Steady States of Disordered Hopping Particle Models with Parallel and Ordered Sequential Dynamics
• Exact Stationary State for an ASEP with Fully Parallel Dynamics
• Asymmetric exclusion process with next-nearest-neighbor interaction: some comments on traffic flow and a nonequilibrium reentrance transition
• Current fluctuations in the zero-range process with open boundaries
• Cumulants and large deviations of the current through non-equilibrium steady states
• Intracellular transport driven by cytoskeletal motors: General mechanisms and defects
• Statistical Physics of Traffic Flow
• Master equations and the theory of stochastic path integrals
• Large deviation functional of the weakly asymmetric exclusion process
• Chaotic properties of systems with Markov dynamics
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Inhomogeneous exclusion processes with extended objects: The effect of defect locations
• Spontaneous Breaking of Translational Invariance in One-Dimensional Stationary States on a Ring
• Current large deviations for Asymmetric Exclusion Processes with open boundaries
• Lee-Yang zeros and phase transitions in nonequilibrium steady states
• Symmetry breaking and phase coexistence in a driven diffusive two-channel system
• Disordered asymmetric simple exclusion process: mean-field treatment
• Bottleneck-induced transitions in a minimal model for intracellular transport
• Towards a model for protein production rates
• Ribosome recycling, diffusion, and mRNA loop formation in translational regulation
• Towards a model for protein production rates
• Microtubule Length-Regulation by Molecular Motors
• A model of hyphal tip growth involving microtubule-based transport
• Mixed population of competing TASEPs with a shared reservoir of particles
• Far-from-equilibrium transport with constrained resources
• Competition between Multiple Totally Asymmetric Simple Exclusion Processes for a Finite Pool of Resources
• Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring: I. The Neutral System
• Efficiency at maximum power of interacting molecular machines
• Current large deviation function for the open asymmetric simple exclusion process
• The asymmetric Exclusion Process and Brownian Excursions
• On U_q(SU(2))-symmetric Driven Diffusion
• An Exact Formula for the Statistics of the Current in the TASEP with Open Boundaries
• Mean field approaches to the totally asymmetric exclusion process with quenched disorder and large particles
• Bethe Ansatz Solution for a Defect Particle in the Asymmetric Exclusion Process
• Exclusion processes on networks as models for cytoskeletal transport
• Phase Transition in the ABC Model
• Finite Dimensional Representations of the Quadratic Algebra: Applications to the Exclusion Process
• The KPZ Limit of ASEP with Boundary
• Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics
• Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
• Asymmetric Exclusion Model and Weighted Lattice Paths
• Boundary-Induced Phase Transitions in Equilibrium and Non-Equilibrium Systems
• A two--parametric family of asymmetric exclusion processes and its exact solution
• Entropy of Open Lattice Systems
• Diffusion algebras
• Matrix-Product States for a One-Dimensional Lattice Gas with Parallel Dynamics
• First-order phase transitions in one-dimensional steady states
• Queuing Transitions in the Asymmetric Simple Exclusion Process
• Relaxation times in the ASEP model using a DMRG method
• Spontaneous symmetry breaking: exact results for a biased random walk model of an exclusion process
• N-species stochastic models with boundaries and quadratic algebras
• Exact solution of a one-parameter family of asymmetric exclusion processes
• Driven Diffusive Systems with Disorder
• Bethe ansatz solution of zero-range process with nonuniform stationary state
• Phase diagram and edge effects in the ASEP with bottlenecks
• Long-Range Order in a Quasi One-Dimensional Non-Equilibrium Three-State Lattice Gas
• Boundary induced phase transitions in driven lattice gases with meta-stable states
• Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
• Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources
• Exact solutions of exactly integrable quantum chains by a matrix product ansatz
• Spontaneous Symmetry Breaking in a Non-Conserving Two-Species Driven Model
• Sample-Dependent Phase Transitions in Disordered Exclusion Models
• Nonequilibrium Dynamics in Low Dimensional Systems
• A dynamically extending exclusion process
• Dynamic correlation functions and Boltzmann Langevin approach for driven one dimensional lattice gas
• Effects of the chemomechanical stepping cycle on the traffic of molecular motors
• The Bethe ansatz as a matrix product ansatz
• Dynamics of an exclusion process with creation and annihilation
• One-dimensional transport of interacting particles: Currents, density profiles, phase diagrams and symmetries
• Weakly coupled, antiparallel, totally asymmetric simple exclusion processes
• Characteristics of the asymmetric simple exclusion process in the presence of quenched spatial disorder
• On the Two Species Asymmetric Exclusion Process with Semi-Permeable Boundaries
• Stochastic boundary conditions in the deterministic Nagel-Schreckenberg traffic model
• Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries
• Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities
• Single-Bottleneck Approximation for Driven Lattice Gases with Disorder and Open Boundary Conditions
• Phase diagram of two-lane driven diffusive systems
• Spontaneous symmetry breaking in a bridge model fed by junctions
• Symmetry breaking through a sequence of transitions in a driven diffusive system
• Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries
• Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics
• Tree structures for the current fluctuations in the exclusion process
• On the ubiquity of matrix-product states in one-dimensional stochastic processes with boundary interactions
• Spurious phase in a model for traffic on a bridge
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries
• Asymmetric simple exclusion processes with diffusive bottlenecks
• Deciphering mRNA Sequence Determinants of Protein Production Rate
• Motor proteins traffic regulation by supply-demand balance of resources
• Long-range attraction between probe particles mediated by a driven fluid
• Hysteresis in one-dimensional reaction-diffusion systems
• Nonequilibrium stationary states and equilibrium models with long range interactions
• Nonequilibrium Criticality at Shock Formation in Steady States
• Infinite reflections of shock fronts in driven diffusive systems with two species
• Global Phase Diagram of a One-Dimensional Driven Lattice Gas
• Spectra of non-hermitian quantum spin chains describing boundary induced phase transitions
• Multiple phase transitions in a system of exclusion processes with limited reservoirs of particles and fuel carriers
• Bethe ansatz solution of discrete time stochastic processes with fully parallel update
• Universal First-Passage-Time Distribution of Non-Gaussian Currents
• Dynamic Boundaries in Asymmetric Exclusion Processes
• One-Dimensional Partially Asymmetric Simple Exclusion Process on a Ring with a Defect Particle
• Deterministic Exclusion Process with a Stochastic Defect: Matrix-Product Ground States
• Bulk and surface transitions in asymmetric simple exclusion process: Impact on boundary layers
• The distribution function of entropy flow in stochastic systems
• Stationary State Skewness in KPZ Type Growth
• Shocks in the asymmetric exclusion process with internal degree of freedom
• Disordered exclusion process revisited: some exact results in the low-current regime
• Driven lattice gas of dimers coupled to a bulk reservoir
• Hydrodynamic limit of multi-chain driven diffusive models
• Power series solution of the inhomogeneous exclusion process
• Dynamical Transition in the Open-boundary Totally Asymmetric Exclusion Process
• Asymmetric simple exclusion process with periodic boundary driving
• Dyck Paths, Motzkin Paths and Traffic Jams
• Collective dynamics on a two-lane asymmetrically coupled TASEP with mutually interactive Langmuir Kinetics
• Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
• Molecular Mechanisms for Microtubule Length Regulation by Kinesin-8 and XMAP215 Proteins
• Boundary-induced abrupt transition in the symmetric exclusion process
• Exclusion Processes and boundary conditions
• Hydrodynamic mean field solutions of 1D exclusion processes with spatially varying hopping rates
• Disordered driven lattice gases with boundary reservoirs and Langmuir kinetics
• Domain wall delocalization, dynamics and fluctuations in an exclusion process with two internal states
• Single-file transport in periodic potentials: The Brownian asymmetric exclusion process
• Asymmetric Simple Exclusion Process with open boundaries and Quadratic Harnesses
• Stochastic thermodynamics in many-particle systems
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• Generalized empty-interval method applied to a class of one-dimensional stochastic models
• A multi-species asymmetric exclusion process;steady state and correlation functions on a periodic lattice
• Modelling bacterial flagellar growth
• Maximum power operation of interacting molecular motors
• The Braess Paradox in a network of totally asymmetric exclusion processes
• Multilane driven diffusive systems
• Robustness of spontaneous symmetry breaking in a bridge model
• Integrable boundary conditions for multi-species ASEP
• Totally asymmetric exclusion process with long-range hopping
• Scaling properties of the asymmetric exclusion process with long-range hopping
• Interplay between finite resources and local defect in an asymmetric simple exclusion process
• Water alignment, dipolar interactions, and multiple proton occupancy during water-wire proton transport
• A reverse duality for the ASEP with open boundaries
• Hydrodynamics of the zero-range process in the condensation regime
• Exclusive Queueing Processes and their Application to Traffic Systems
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Braess paradox in a network with stochastic dynamics and fixed strategies
• Diffusion of tagged particles in a crowded medium
• Fixed points and boundary layers in exclusion processes
• Phase transitions in systems possessing Shock solutions
• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• Operon Dynamics with State Dependent Transcription and/or Translation Delays
• Dynamics at barriers in bidirectional two-lane exclusion processes
• Exact Shock Profile for the ASEP with Sublattice-Parallel Update
• Limit fluctuations for density of asymmetric simple exclusion processes with open boundaries
• Matrix product solution to a 2-species TASEP with open integrable boundaries
• Dynamic Singularities in Cooperative Exclusion
• On the solvable multi-species reaction-diffusion processes
• Frozen shuffle update for an asymmetric exclusion process with open boundary conditions
• Effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks
• Power Spectra of a Constrained Totally Asymmetric Simple Exclusion Process
• The repton model of gel electrophoresis
• Relaxation rate of the reverse biased asymmetric exclusion process
• Competing Glauber and Kawasaki Dynamics
• The effect of detachment and attachment to a kink motion in the asymmetric simple exclusion process
• Open ASEP in the Weakly Asymmetric Regime
• Work and heat probability distributions in out-of-equilibrium systems
• Pinned or moving: states of a single shock in a ring
• Exact Solution of Two-Species Ballistic Annihilation with General Pair-Reaction Probability
• Power series method for solving TASEP-based models of mRNA translation
• Combinatorial mappings of exclusion processes
• Understanding the edge effect in TASEP with mean-field theoretic approaches
• Long time asymptotics of the totally asymmetric simple exclusion process
• Efficiency at maximum power of motor traffic on networks
• Annihilation-diffusion processes: an exactly solvable model
• Unusual shock wave in two-species driven systems with an umbilic point
• Ergodicity breaking in one-dimensional reaction-diffusion systems
• Multi shocks in Reaction-diffusion models
• Dynamics of ribosomes in mRNA translation under steady and non-steady state conditions
• On the absorbing-state phase transition in the one-dimensional triplet creation model
• Stochastic modelling of collective motor protein transport through a crossing of microtubules
• Finite-size scaling in the steady state of the fully asymmetric exclusion process
• Infinitely-fast diffusion in Single-File Systems
• Multi-state asymmetric simple exclusion processes
• Matrix product solution to multi-species ASEP with open boundaries
• Dynamical scaling for probe particles in a driven fluid
• An exclusion process on a tree with constant aggregate hopping rate
• Persistent random walk with exclusion
• Dynamical transition in the TASEP with Langmuir kinetics: mean-field theory
• Exact domain wall theory for deterministic TASEP with parallel update
• Current-density relation in the exclusion process with dynamic obstacles
• An introduction to phase transitions in stochastic dynamical systems
• Surface critical behavior of driven diffusive systems with open boundaries
• Duality and phase diagram of one dimensional transport
• A Remark on Integrability of Stochastic Systems Solvable by Matrix Product Ansatz
• Cluster approximations for the TASEP: stationary state and dynamical transition
• Exact stationary state for a deterministic high speed traffic model with open boundaries
• Transient behavior in Single-File Systems
• On the blockage problem and the non-analyticity of the current for the parallel TASEP on a ring
• Matrix product solution of a left-permeable two-species asymmetric exclusion process
• Exclusion in a priority queue
• Renyi entropy of the totally asymmetric exclusion process
• Localisation Transition of A Dynamic Reaction Front
• Competition for finite resources
• Exclusion Process on two intersected lanes with constrained resources: Symmetry breaking and shock dynamics
• Renormalized field theory and particle density profile in driven diffusive systems with open boundaries
• Two-species active transport along cylindrical biofilaments is limited by emergent topological hindrance
• Matrix product solution for a partially asymmetric 1D lattice gas with a free defect
• Solution of a one-dimensional stochastic model with branching and coagulation reactions
• Unbalanced Langmuir kinetics affects TASEP dynamical transitions: mean-field theory
• Brownian ratchets driven by asymmetric nucleation of hydrolysis waves
• The blockage problem
• Analytical Approach to the One-Dimensional Disordered Exclusion Process with Open Boundaries and Random Sequential Dynamics
• Numerical survey of the tunable condensate shape and scaling laws in pair-factorized steady states
• Condensation transition in zero-range processes with diffusion
• Effects of a local defect on one-dimensional nonlinear surface growth
• Collective Effects in Models for Interacting Molecular Motors and Motor-Microtubule Mixtures
• Asymmetric exclusion processes on a closed network with bottlenecks
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
• Out-of-equilibrium Frenkel-Kontorova model
• One-dimensional irreversible aggregation with TASEP dynamics
• An anti-symmetric exclusion process for two particles on an infinite 1D lattice
• KPZ fluctuations in finite volume
• Shocks in asymmetric simple exclusion processes of interacting particles
• Asymmetric Exclusion Process with Global Hopping
• Statistics of sums of correlated variables described by a matrix product ansatz
• Shock of three-state model for intracellular transport of kinesin KIF1A
• Exclusion model of mRNA translation with collision-induced ribosome drop-off
• Askey-Wilson signed measures and open ASEP in the shock region
• Nonequilibrium transport and phase transitions in driven diffusion of interacting particles
• Exact density profiles for fully asymmetric exclusion process with discrete-time dynamics
• Parallel updating cellular automaton models of driven diffusive Frenkel-Kontorova-type systems
• Metastability and spinodal points for a random walker on a triangle
• $T$-$Q$ relations for the integrable two-species asymmetric simple exclusion process with open boundaries
• Totally Asymmetric Exclusion Process with Hierarchical Long-Range Connections
• From Quantum Affine Symmetry to Boundary Askey-Wilson Algebra and Reflection Equation
• Coupling driven exclusion and diffusion processes on parallel lanes: boundary induced phase transitions and boundary layers
• One-dimensional discrete aggregation-fragmentation model
• Domain wall of the totally asymmetric exclusion process without particle number conservation
• Dynamical transitions in a driven diffusive model with interactions
• Particle creation and annihilation in an exclusion process on networks
• Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP
• The fitness landscapes of translation
• A Position-Space Renormalization-Group Approach for Driven Diffusive Systems Applied to the Asymmetric Exclusion Model
• Transverse Temperature Interfaces in the Katz-Lebowitz-Spohn Driven Lattice Gas
• Mass transport perspective on an accelerated exclusion process: Analysis of augmented current and unit-velocity phases
• Translational control of gene expression via interacting feedback loops
• Random sparse generators of Markovian evolution and their spectral properties
• Nonequilibrium tricriticality in one dimension
• A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour
• Optimizing evacuation flow in a two-channel exclusion process
• A two-line representation of stationary measure for open TASEP
• Condensation transition in a model with attractive particles and non-local hops
• Impurity-induced shocks in the asymmetric exclusion process with long-range hopping
• Transfer matrices for the totally asymmetric exclusion process
• Boundary induced phase transition with stochastic entrance and exit
• Realization of the open-boundary totally asymmetric simple exclusion process on a ring
• Approach to stationarity for the KPZ fixed point with boundaries
• Boundary-driven phase transitions in open two-species driven systems with an umbilic point
• Local resetting with geometric confinement
• Numerical Estimation of the Current Large Deviation Function in the Asymmetric Simple Exclusion Process with Open Boundary Conditions
• Asymmetric simple exclusion process in one-dimensional chains with long-range links
• Exclusion process on an open lattice with fluctuating boundaries
• A two-species d-dimensional diffusive model and its mapping onto a growth model
• Phase coexistence phenomena in an extreme case of the misanthrope process with open boundaries
• Translation with frameshifting of ribosome along mRNA transcript
• Absence of phase coexistence in disordered exclusion processes with bypassing
• Renormalization group analysis for an asymmetric simple exclusion process
• Stationary measure for six-vertex model on a strip
• Parallel Temperature Interfaces in the Katz-Lebowitz-Spohn Driven Lattice Gas
• Weak pinning and long-range anticorrelated motion of phase boundaries in driven diffusive systems
• Kinetic induced phase transition
• Correlations of density and current fluctuations in single-file motion of hard spheres and in driven lattice gas with nearest-neighbor interaction
• Existence and uniqueness of solution of the differential equation describing the TASEP-LK coupled transport process
• Nonequilibrium phase transition in single-file transport at high crowding
• Exact solution of the Glauber-Ising model on the finite-length semi-open chain
• A Novel Mechanism of Ordering in a Coupled Driven System: Vacancy Induced Phase Separation
• Hidden Symmetries of Stochastic Models
• Emergent centrality in rank-based supplanting process
• Steady-state dynamics of exclusion process with local reversible association of particles
• Fluctuations in meta-population exclusion processes
• Theoretical analysis of transcription process with polymerase stalling
• Steady state representations for the harmonic process
• Limit fluctuations of stationary measure of totally asymmetric simple exclusion process with open boundaries on the coexistence line
• Limits of open ASEP stationary measures near a boundary