Asymptotics for the Norm of Bethe Eigenstates in the Periodic Totally Asymmetric Exclusion Process
Résumé
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 ∼ 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.
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