On the Existence of Monodromies for the Rabi model

Abstract

We discuss the existence of monodromies associated with the singular points of the eigenvalue problem for the Rabi model. The complete control of the full monodromy data requires the taming of the Stokes phenomenon associated with the unique irregular singular point. The monodromy data, in particular the composite monodromy, are written in terms of the parameters of the model via the isomonodromy method and the tau-function of the Painlevé V. These data provide a systematic way to obtain the quantized spectrum of the Rabi model.

6 pages, two-columns

References in corpus (5)

• Integrability vs exact solvability in the quantum Rabi and Dicke models
• Analytical method of spectra calculations in the Bargmann representation
• An exactly solvable system from quantum optics
• Isomonodromy, Painlevé Transcendents and Scattering off of Black Holes
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Cited by in corpus (8)

• Monodromy dependence and connection formulae for isomonodromic tau functions
• Irregular conformal blocks and connection formulae for Painlevé V functions
• Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model
• Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes
• Quantum spectral problems and isomonodromic deformations
• Expansions for semiclassical conformal blocks
• Density-functional theory for the Dicke Hamiltonian
• Stokes graphs of the Rabi problem with real parameters