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Phys. Rev. Lett. 95, 240601 (2005) [4 pages]

Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries

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Jan de Gier1 and Fabian H. L. Essler2
1Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne, 3010 VIC, Australia
2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom

Received 31 August 2005; published 8 December 2005

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.

© 2005 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.95.240601
DOI:
10.1103/PhysRevLett.95.240601
PACS:
05.70.Ln, 02.50.Ey, 75.10.Pq