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arXiv · hep-th/9812211

Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations

Patrick Dorey·Roberto Tateo
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Abstract

The spectral determinant $D(E)$ of the quartic oscillator is known to satisfy a functional equation. This is mapped onto the $A_3$-related $Y$-system emerging in the treatment of a certain perturbed conformal field theory, allowing us to give an alternative integral expression for $D(E)$. Generalising this result, we conjecture a relationship between the $x^{2M}$ anharmonic oscillators and the $A_{2M-1}$ TBA systems. Finally, spectral determinants for general $|x|^α$ potentials are mapped onto the solutions of nonlinear integral equations associated with the (twisted) XXZ and sine-Gordon models.

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Patrick Dorey, Roberto Tateo. 1998-12-22. Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations. https://doi.org/10.1088/0305-4470%2F32%2F38%2F102

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