Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries

Details Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries

2008-06-21

arxiv.org/abs/0806.3493v2

J. Phys. A: Math. Theor. 41 (2008), 485002 (25pp)

Physics

Condensed Matter

Statistical Mechanics

30 pages, 9 figures, typeset for pdflatex; revised version

Scientific paper

10.1088/1751-8113/41/48/485002

We analyze the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process on a finite lattice and with the most general open boundary conditions. We extend results obtained recently for totally asymmetric diffusion [J. de Gier and F.H.L. Essler, J. Stat. Mech. P12011 (2006)] to the case of partial symmetry. We determine the finite-size scaling of the spectral gap, which characterizes the approach to stationarity at large times, in the low and high density regimes and on the coexistence line. We observe boundary induced crossovers and discuss possible interpretations of our results in terms of effective domain wall theories.

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