Extrapolation methods and Bethe ansatz for the asymmetric exclusion process

Abstract

The one-dimensional asymmetric simple exclusion process (ASEP), where $N$ hard-core particles hop forward with rate $1$ and backward with rate $q<1$, is considered on a periodic lattice of $L$ site. Using KPZ universality and previous results for the totally asymmetric model $q=0$, precise conjectures are formulated for asymptotics at finite density $\rho =N/L$ of ASEP eigenstates close to the stationary state. The conjectures are checked with high precision using extrapolation methods on finite size Bethe ansatz numerics. For weak asymmetry $1-q\sim 1/\sqrt{L}$, double extrapolation combined with an integer relation algorithm gives an exact expression for the spectral gap up to $10$-th order in the asymmetry.

21 pages, 4 figures, 1 table

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Cited by in corpus (8)

• Riemann surfaces for KPZ with periodic boundaries
• Ground state energy of the $\delta$-Bose and Fermi gas at weak coupling from double extrapolation
• Integral formulas of ASEP and $q$-TAZRP on a ring
• Perturbative solution for the spectral gap of the weakly asymmetric exclusion process
• KPZ fluctuations in finite volume
• Riemann surfaces for integer counting processes
• From the Riemann surface of TASEP to ASEP
• Effects of Quantum Pair Creation and Annihilation on a Classical Exclusion Process: the transverse XY model with TASEP