Extrapolation methods and Bethe ansatz for the asymmetric exclusion process
Résumé
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 ρ=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∼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.