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

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

1998-12-22

arxiv.org/abs/hep-th/9812211v1

J.Phys.A32:L419-L425,1999

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, Latex 2e, uses amssymb, cite

Scientific paper

10.1088/0305-4470/32/38/102

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.

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