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

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 $|x{|}^{\alpha }$ potentials are mapped onto the solutions of nonlinear integral equations associated with the (twisted) XXZ and sine-Gordon models.

11 pages, Latex 2e, uses amssymb, cite

References in corpus (2)

• On nonequilibrium states in QFT model with boundary interaction
• Airy function (exact WKB results for potentials of odd degree)

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