Jan de Gier and Fabian H L Essler J. Stat. Mech. (2006) P12011 doi:10.1088/1742-5468/2006/12/P12011
Exact spectral gaps of the asymmetric exclusion process with open boundaries
FREE ARTICLE Topical articles on The 75th Anniversary of the Bethe AnsatzJan de Gier1 and Fabian H L Essler2
Show affiliationsPart of Topical articles on The 75th Anniversary of the Bethe Ansatz
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.
- Keywords
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driven diffusive systems (theory)
- PACS
- MSC
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82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium)
- Subjects
- Dates
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Issue 12 (December 2006)
Received 25 September 2006, accepted for publication 18 November 2006
Published 14 December 2006
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Exact spectral gaps of the asymmetric exclusion process with open boundaries
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