Asymptotics for the norm of Bethe eigenstates in the periodic totally asymmetric exclusion process

Abstract

The normalization of Bethe eigenstates for the totally asymmetric simple exclusion process on a ring of $L$ sites is studied, in the large $L$ limit with finite density of particles, for all the eigenstates responsible for the relaxation to the stationary state on the KPZ time scale $T\sim L^{3/2}$. In this regime, the normalization is found to be essentially equal to the exponential of the action of a scalar free field. The large $L$ asymptotics is obtained using the Euler-Maclaurin formula for summations on segments, rectangles and triangles, with various singularities at the borders of the summation range.

32 pages, 2 figures; J. Stat. Phys. (2015)

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Cited by in corpus (8)

• Finite-time fluctuations for the totally asymmetric exclusion process
• Riemann surfaces for KPZ with periodic boundaries
• Integral formulas of ASEP and $q$-TAZRP on a ring
• Extrapolation methods and Bethe ansatz for the asymmetric exclusion process
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Perturbative solution for the spectral gap of the weakly asymmetric exclusion process
• Brownian bridges for late time asymptotics of KPZ fluctuations in finite volume
• KPZ fluctuations in finite volume