Integrability of the Rabi model.

  title={Integrability of the Rabi model.},
  author={Daniel Braak},
  journal={Physical review letters},
  volume={107 10},
  • D. Braak
  • Published 12 March 2011
  • Physics
  • Physical review letters
The Rabi model is a paradigm for interacting quantum systems. It couples a bosonic mode to the smallest possible quantum model, a two-level system. I present the analytical solution which allows us to consider the question of integrability for quantum systems that do not possess a classical limit. A criterion for quantum integrability is proposed which shows that the Rabi model is integrable due to the presence of a discrete symmetry. Moreover, I introduce a generalization with no symmetries… 

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  • R. Rosenfeld
  • Medicine
    Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery
  • 2009


  • Rev. A 41, 5666
  • 1990


  • Pure Appl. Math. 14, 197
  • 1961


  • Rev. Lett. 90, 044101
  • 2003

Phys. Rev. Lett

  • Phys. Rev. Lett
  • 2003

Phys. Rev. Lett

  • Phys. Rev. Lett
  • 2010

Phys. Rev. Lett

  • Phys. Rev. Lett
  • 2007


  • Rev. Lett. 54, 1343
  • 1985