2006/09/30 by Jan de Gier, Fabian H L Essler · 151 citations
Mathematics · Physics and Astronomy · #Ansatz #Bethe ansatz #Boundary (topology) #Interpretation (philosophy) #Matrix (chemical analysis) #Oscillation (cell signaling) #Quantum many-body systems #Scaling #Spectral gap #Spectrum (functional analysis) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2006/12/p12011
published in Journal of Statistical Mechanics Theory and Experiment 2006(12), P12011 (Institute of Physics) · 42 pages, 25 figures; added appendix and minor corrections
arxiv created 2006/11/21 · arxiv updated 2009/12/01
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 (Kardar–Parisi–Zhang) 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 . 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.