1999/06/15 by Paul Fendley
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #nlin.SI #solv-int
published as Lett.Math.Phys. 49 (1999) 229-233 · 4 pages
arxiv created 1999/06/15 · arxiv updated 2009/11/30
Thermodynamic Bethe ansatz equations are coupled non-linear integral equations which appear frequently when solving integrable models. Those associated with models with N=2 supersymmetry can be related to differential equations, among them Painleve III and the Toda hierarchy. In the simplest such case the massless limit of these non-linear integral equations can be solved in terms of the Airy function. This is the only known closed-form solution of thermodynamic Bethe ansatz equations, outside of free or classical models. This turns out to give the spectral determinant of the Schrodinger equation in a linear potential.