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

O. Golinelli·K. Mallick
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Abstract

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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O. Golinelli, K. Mallick. 2003-12-15. Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process. https://doi.org/10.1088/0305-4470%2F37%2F10%2F001

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