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Airy functions in the thermodynamic Bethe ansatz
High Energy Physics - Theory · Submitted 15 Jun 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In the simplest such case the massless limit of these non-linear integral equations can be solved in terms of the Airy function.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Thermodynamic Bethe ansatz equations are coupled non-linear integral equations which appear frequently when solving integrable models. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s1 | Those associated with models with N=2 supersymmetry can be related to differential equations, among them Painleve III and the Toda hierarchy. | background 0.99 | 0.16 | 0.05 | asserted 0.86 |
| s2 | In the simplest such case the massless limit of these non-linear integral equations can be solved in terms of the Airy function. | result 0.86 | 0.38 | 0.61 | asserted 0.99 |
| s3 | This is the only known closed-form solution of thermodynamic Bethe ansatz equations, outside of free or classical models. | result 0.48 | 0.22 | 0.41 | asserted 1.00 |
| s4 | This turns out to give the spectral determinant of the Schrodinger equation in a linear potential. | interpretation 0.74 | 0.65 | 0.25 | asserted 1.00 |
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Original abstract
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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3 arXiv papers cite this in 3 sentences
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We will call $$ the Airy operator, since it is closely related to the Airy functions (see e.g. [ref] ).
New renormalons from analytic trans-series · Acknowledgements · 0.99
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