Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries

2005/08/31 by Jan de Gier, Fabian H. L. Essler, Fabian H. L. Eßler · 8 citations
Mathematics · Physics and Astronomy · #Ansatz #Bethe ansatz #Boundary (topology) #Boundary value problem #Diffusion #Integrable system #Materials science #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Quantum mechanics #Random Matrices and Applications #Scaling #Spectral gap #Spectrum (functional analysis) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.95.240601

published as Phys. Rev. Lett. 95 (2005), 240601 · 4 pages, 2 figures, published version

openalex publication_date 2005/12/08 · arxiv created 2005/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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. For totally asymmetric diffusion we calculate the spectral gap, which characterizes the approach to stationarity at large times. We observe boundary induced crossovers in and between massive, diffusive, and Kardar-Parisi-Zhang scaling regimes.

Citations

• Magic in the spectra of the XXZ quantum chain with boundaries at Δ=0 and Δ=−1/2
• The surface statistics of a granular aggregate
• Integrable XYZ Spin Chain with Boundaries
• Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries
• Bethe ansatz calculation of the spectral gap of the asymmetric exclusion process
• Statistical Physics of Vehicular Traffic and Some Related Systems

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