Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries

Abstract

We analyze the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process on a finite lattice and with the most general open boundary conditions. We extend results obtained recently for totally asymmetric diffusion [J. de Gier and F.H.L. Essler, J. Stat. Mech. P12011 (2006)] to the case of partial symmetry. We determine the finite-size scaling of the spectral gap, which characterizes the approach to stationarity at large times, in the low and high density regimes and on the coexistence line. We observe boundary induced crossovers and discuss possible interpretations of our results in terms of effective domain wall theories.

30 pages, 9 figures, typeset for pdflatex; revised version

References in corpus (32)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Phase transitions in an exactly soluble one-dimensional exclusion process
• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Fluctuation properties of the TASEP with periodic initial configuration
• Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Partially Asymmetric Exclusion Process with Open Boundaries
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Functional relations and Bethe Ansatz for the XXZ chain
• Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra
• Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries
• Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Correlation functions of the open XXZ chain I
• An integrable structure related with tridiagonal algebras
• Q-operator and T-Q relation from the fusion hierarchy
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• Spectral gap of the totally asymmetric exclusion process at arbitrary filling
• Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
• Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• Relaxation times in the ASEP model using a DMRG method
• Dynamic correlation functions and Boltzmann Langevin approach for driven one dimensional lattice gas
• Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries
• Bethe Ansatz derived from the functional relations of the open XXZ chain for new special cases
• Current Fluctuations in the exclusion process and Bethe Ansatz
• The Asymmetric Avalanche Process
• Power-law behavior in the power spectrum induced by Brownian motion of a domain wall
• Real-space renormalisation group approach to driven diffusive systems
• Generalized T-Q relations and the open XXZ chain

Cited by in corpus (35)

• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
• Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Current large deviation function for the open asymmetric simple exclusion process
• Integrability of $1D$ Lindbladians from operator-space fragmentation
• Yang-Baxter integrable Lindblad equations
• Some Exact Results for the Exclusion Process
• Bethe Ansatz for the Weakly Asymmetric Simple Exclusion Process and phase transition in the current distribution
• Cumulants of the current in the weakly asymmetric exclusion process
• Tree structures for the current fluctuations in the exclusion process
• Bethe Ansatz and Q-operator for the open ASEP
• Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model
• Dynamical Transition in the Open-boundary Totally Asymmetric Exclusion Process
• Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Continued Fractions and the Partially Asymmetric Exclusion Process
• Relaxation rate of the reverse biased asymmetric exclusion process
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Perturbative solution for the spectral gap of the weakly asymmetric exclusion process
• Cluster approximations for the TASEP: stationary state and dynamical transition
• Limiting current distribution for a two species asymmetric exclusion process
• Integrability of two-species partially asymmetric exclusion processes
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• Lifted TASEP: a Bethe ansatz integrable paradigm for non-reversible Markov chains
• KPZ fluctuations in finite volume
• $T$-$Q$ relations for the integrable two-species asymmetric simple exclusion process with open boundaries
• Dynamical transitions in a driven diffusive model with interactions
• Totally asymmetric simple exclusion process with local resetting and open boundary conditions
• Random sparse generators of Markovian evolution and their spectral properties
• Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation
• Optimizing evacuation flow in a two-channel exclusion process
• Stroboscopic exclusion process: a first-moment-driven dynamics
• Fluctuations in meta-population exclusion processes
• Lifted TASEP: long-time dynamics,generalizations, and continuum limit