Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries

Abstract

We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. By analysing these equations in detail for the cases of totally asymmetric and symmetric diffusion, we calculate the finite-size scaling of the spectral gap, which characterizes the approach to stationarity at large times. In the totally asymmetric case we observe boundary induced crossovers between massive, diffusive and KPZ scaling regimes. We further study higher excitations, and demonstrate the absence of oscillatory behaviour at large times on the ``coexistence line'', which separates the massive low and high density phases. In the maximum current phase, oscillations are present on the KPZ scale $t\propto L^{-3/2}$. While independent of the boundary parameters, the spectral gap as well as the oscillation frequency in the maximum current phase have different values compared to the totally asymmetric exclusion process with periodic boundary conditions. We discuss a possible interpretation of our results in terms of an effective domain wall theory.

arXiv comment42 pages, 25 figures; added appendix and minor corrections

References in corpus (36)

• Statistical Physics of Vehicular Traffic and Some Related Systems
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation theorem for stochastic dynamics
• Dynamical ensembles in stationary states
• 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
• Exact scaling functions for one-dimensional stationary KPZ growth
• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries
• Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
• Partially 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
• Current fluctuations in the zero-range process with open boundaries
• Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Integrable XYZ Spin Chain with Boundaries
• Large deviation functional of the weakly asymmetric exclusion process
• Upper critical dimension, dynamic exponent and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation
• Q-operator and T-Q relation from the fusion hierarchy
• Magic in the spectra of the XXZ quantum chain with boundaries at Delta=0 and Delta=-1/2
• Spectral gap of the totally asymmetric exclusion process at arbitrary filling
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• 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
• Relaxation times in the ASEP model using a DMRG method
• Dynamic correlation functions and Boltzmann Langevin approach for driven one dimensional lattice gas
• Equivalences between spin models induced by defects
• Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries
• The Asymmetric Avalanche Process
• Crossover Scaling Functions in One Dimensional Dynamic Growth Models
• Power-law behavior in the power spectrum induced by Brownian motion of a domain wall
• Spectral Degeneracies in the Totally Asymmetric Exclusion Process
• Numerical Solution of the Mode-Coupling Equations for the Kardar-Parisi-Zhang Equation in One Dimension

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