arXiv:1703.04596 · Journal of Physics A Mathematical and Theoretical

Perturbative solution for the spectral gap of the weakly asymmetric exclusion process

Sylvain Prolhac

Published Jun 7, 2017• 15 citations

Abstract

Abstract We consider the weakly asymmetric exclusion process with N = L / 2 particles on a periodic lattice of L sites and hopping rates 1 and q = 1 − μ / L in the forward and in the backward direction respectively. Using the Bethe ansatz, we obtain a systematic perturbative expansion of the spectral gap near μ = 0 by solving a simple functional equation order by order. A key point is that when μ → 0 , Bethe roots at a distance 1 / L from the edge of the Fermi sea should not be considered as a continuum but converge instead at large L to the complex zeroes of 1 + e r f ( x ) after a rescaling by L .

DOI: 10.1088/1751-8121/aa77de

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