On the Rabi Model and its Generalizations

The Rabi model is shown to be only a particular case of a generic class R of models characterized by the following properties:
(i) wave function Ψ(E,x) is the generating function for orthogonal polynomials φ_n(E) of a discrete energy variable E;
(ii) any model of R has nondegenerate purely point spectrum that corresponds to infinite discrete support of measure dν in the orthogonality relation of the polynomials φ_n;
(iii) the support is determined exclusively by the points of discontinuity of dν(E);
(iv) the spectrum can be numerically determined as fixed points of monotonic flows of the zeros of orthogonal polynomials φ_n(E);
(v) one can compute practically an unlimited number of energy levels;
(vi) the spectrum of exactly solvable models from R can only assume one of four qualitatively different types.

[1] A. Moroz, Europhys. Lett.100, 60010 (2012); Ann. Phys. (N.Y.) 338, 319 (2013); ibid. 340, 252 (2014); ibid. 351, 960 (2014); J. Phys. A: Math. Theor. 47, 495204 (2014).

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