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

2014/11/30 by Sylvain Prolhac · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1007/s10955-015-1230-0

published as J. Stat. Phys. 160 (2015) 926-964 · 32 pages, 2 figures; J. Stat. Phys. (2015)

arxiv created 2015/03/16 · arxiv updated 2015/07/31

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∼ 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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