Exact Current Statistics of the ASEP with Open Boundaries

Abstract

Non-equilibrium systems are often characterized by the transport of some quantity at a macroscopic scale, such as, for instance, a current of particles through a wire. The Asymmetric Simple Exclusion Process (ASEP) is a paradigm for non-equilibrium transport that is amenable to exact analytical solution. In the present work, we determine the full statistics of the current in the finite size open ASEP for all values of the parameters. Our exact analytical results are checked against numerical calculations using DMRG techniques.

5 pages, references added

References in corpus (13)

• The density-matrix renormalization group in the age of matrix product states
• The large deviation approach to statistical mechanics
• 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
• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• Far-from-equilibrium transport with constrained resources
• DMRG-study of current and activity fluctuations near non-equilibrium phase transitions
• Matrix product solution of the multispecies partially asymmetric exclusion process
• From interacting particle systems to random matrices
• Total Current Fluctuations in ASEP

Cited by in corpus (85)

• Dissipation bounds all steady-state current fluctuations
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• Matrix product solutions of boundary driven quantum chains
• Run-and-tumble in a crowded environment: persistent exclusion process for swimmers
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
• A minimal model of dynamical phase transition
• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Exact large-deviation statistics for a nonequilibrium quantum spin chain
• Singularities in large deviation functions
• Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with Exclusion
• The inverse scattering of the Zakharov-Shabat system solves the weak noise theory of the Kardar-Parisi-Zhang equation
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Finite-time fluctuations for the totally asymmetric exclusion process
• Exactly solvable counting statistics in weakly coupled open interacting spin systems
• Systematic time expansion for the Kardar-Parisi-Zhang equation, linear statistics of the GUE at the edge and trapped fermions
• Large-deviation statistics of a diffusive quantum spin chain and the additivity principle
• Dynamical phase transitions in the current distribution of driven diffusive channels
• Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure
• Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder
• Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
• Distinct universality classes of diffusive transport from full counting statistics
• Sampling rare events across dynamical phase transitions
• Bethe Ansatz and Q-operator for the open ASEP
• Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries
• Self-Sustained Density Oscillations of Swimming Bacteria Confined in Microchambers
• Dynamical Phase Transitions in a 2D Classical Nonequilibrium Model via 2D Tensor Networks
• Current fluctuations in boundary-driven quantum spin chains
• Minimal model of transcriptional elongation processes with pauses
• Optimal sampling of dynamical large deviations in two dimensions via tensor networks
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Residence time estimates for asymmetric simple exclusion dynamics on stripes
• Non-Gaussian anomalous dynamics in systems of interacting run-and-tumble particles
• Effective Hamiltonians and Lagrangians for conditioned Markov processes at large volume
• Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary
• Emergence of jams in the generalized totally asymmetric simple exclusion process
• Integrable boundary conditions for multi-species ASEP
• Weak additivity principle for current statistics in d-dimensions
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Full counting statistics and the Edgeworth series for matrix product states
• Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries
• Fluctuations in interacting particle systems with memory
• Riemann surfaces for KPZ with periodic boundaries
• Large deviations in the symmetric simple exclusion process with slow boundaries
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice - bulk eigenvalues
• Efficiency of one-dimensional active transport conditioned on motility
• Extrapolation methods and Bethe ansatz for the asymmetric exclusion process
• Open ASEP in the Weakly Asymmetric Regime
• Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization
• Equivalent T-Q relations and exact results for the open TASEP
• Current large deviations for partially asymmetric particle systems on a ring
• Singularities in Large Deviation Functionals of Bulk-Driven Transport Models
• Dynamics of ribosomes in mRNA translation under steady and non-steady state conditions
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Riemann surface for TASEP with periodic boundaries
• Rate dependence of current and fluctuations in jump models with negative differential mobility
• Lower current large deviations for zero-range processes on a ring
• Asymptotics for the norm of Bethe eigenstates in the periodic totally asymmetric exclusion process
• Transport in exclusion processes with one-step memory: density dependence and optimal acceleration
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
• Assisted exchange models in one dimension
• Two-species active transport along cylindrical biofilaments is limited by emergent topological hindrance
• Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
• Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• KPZ fluctuations in finite volume
• Universality and non-universality of mobility in heterogeneous single-file systems and Rouse chains
• Current fluctuations for totally asymmetric exclusion on the relaxation scale
• On matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the singular case
• Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study
• Full absorption statistics of diffusing particles with exclusion
• Self-duality and shock dynamics in the $n$-component priority ASEP
• Particle current fluctuations in a variant of asymmetric Glauber model
• Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP
• Current statistics in the q-boson zero range process
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Approach to stationarity for the KPZ fixed point with boundaries
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions
• Restricted permutations for the simple exclusion process in discrete time over graphs
• Current fluctuations for the second class particle : joint statistics
• Nonequilibrium phases and quantum correlations in synthetic transport models
• Structure of the optimal path to a fluctuation
• Crossover scaling functions in the asymmetric avalanche process