Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process

Details Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process

2003-12-15

arxiv.org/abs/cond-mat/0312371v1

J. Phys. A: Math. Gen. 37 (2004) 3321-3331

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1088/0305-4470/37/10/001

We present a new derivation of the spectral gap of the totally asymmetric exclusion process on a half-filled ring of size L by using the Bethe Ansatz. We show that, in the large L limit, the Bethe equations reduce to a simple transcendental equation involving the polylogarithm, a classical special function. By solving that equation, the gap and the dynamical exponent are readily obtained. Our method can be extended to a system with an arbitrary density of particles. Keywords: ASEP, Bethe Ansatz, Dynamical Exponent, Spectral Gap.

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