Airy functions in the thermodynamic Bethe ansatz

Details Airy functions in the thermodynamic Bethe ansatz Airy functions in the thermodynamic Bethe ansatz

1999-06-15

arxiv.org/abs/hep-th/9906114v1

Lett.Math.Phys. 49 (1999) 229-233

Physics

High Energy Physics

High Energy Physics - Theory

4 pages

Scientific paper

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.

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