Integrability of the Rabi model.

@article{Braak2011IntegrabilityOT,
  title={Integrability of the Rabi model.},
  author={Daniel Braak},
  journal={Physical review letters},
  year={2011},
  volume={107 10},
  pages={
          100401
        }
}
  • 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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References

SHOWING 1-10 OF 54 REFERENCES

Integrable Models in Condensed Matter Physics

This is an expanded version of the lectures given at the Trieste Summer School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter Physicists.

Modern foundations of quantum optics

From Geometry to the Quantum Introduction to Lasers Properties of Light: Blackbody Radiation Interaction of Light with Matter I Basic Optical Processes -- Still Classical More Detailed Principles of

Phys

  • Rev. A 41, 5666
  • 1990

Comm

  • Pure Appl. Math. 14, 197
  • 1961

Phys

  • 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

Phys

  • Rev. Lett. 54, 1343
  • 1985

Modern Foundations of Quantum Optics (Imperial

  • 2006
...