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

2003/12/15 by O. Golinelli, O Golinelli, K. Mallick +1 · 5 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Random Matrices and Applications #Stochastic processes and statistical mechanics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1088/0305-4470/37/10/001

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

arxiv created 2003/12/15 · openalex publication_date 2004/02/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

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.

Citations

• The Bethe ansatz as a matrix product ansatz
• Bethe ansatz solution for a defect particle in the asymmetric exclusion process

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