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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. 1

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We suggest an approach to the problem of finding integral equations for the excited states of an integrable model, starting from the Thermodynamic Bethe Ansatz equations for its ground state. The idea relies on analytic continuation through complex values of the coupling constant, and an analysis of the monodromies that the equations and their solutions undergo. For the scaling Lee-Yang model, we find equations in this way for the one-and two-particle states in the spin-zero sector, and suggest various generalisations. Numerical results show excellent agreement with the truncated conformal space approach, and we also treat some of the ultraviolet and infrared asymptotics analytically.

This article reviews a recently-discovered link between integrable quantum field theories and certain ordinary differential equations in the complex domain. Along the way, aspects of PT -symmetric quantum mechanics are discussed, and some elementary features of the six-vertex model and the Bethe ansatz are explained.

The appearances of complex eigenvalues in the spectra of PT -symmetric quantummechanical systems are usually associated with a spontaneous breaking of PT . In this letter we discuss a family of models for which this phenomenon is also linked with an explicit breaking of supersymmetry. Exact level-crossings are located, and connections with N -fold supersymmetry and quasi-exact solvability in certain special cases are pointed out.

The aim of these notes is to provide an elementary introduction to some of the basic elements of exact S-matrix theory. This is a large subject, and only the beginnings will be covered here. A particular omission is any serious discussion of the Yang-Baxter equation; instead, the focus will be on questions of analytic structure, and the bootstrap equations. Even then, what I have to say will only be a sketch of the simpler aspects. The hope is to give a hint of the many curious features of scattering theories in 1+1 dimensions.DTP-98/69; hep-th/9810026

We study kink-antikink collisions in the one-dimensional nonintegrable scalar φ⁶ model. Although the single-kink solutions for this model do not possess an internal vibrational mode, our simulations reveal a resonant scattering structure, thereby providing a counterexample to the standard belief that the existence of such a mode is a necessary condition for multibounce resonances in general kink-antikink collisions. We investigate the two-bounce windows in detail, and present evidence that this structure is caused by the existence of bound states in the spectrum of small oscillations about a combined kink-antikink configuration.