The spectral determinant D(E) of the quartic oscillator is known to satisfy a functional equation. This is mapped onto the A3-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 x2M anharmonic oscillators and the A2M−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.
Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
TATEO, Roberto
1999-01-01
Abstract
The spectral determinant D(E) of the quartic oscillator is known to satisfy a functional equation. This is mapped onto the A3-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 x2M anharmonic oscillators and the A2M−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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