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Hamiltonian analysis of exact integrability of the quantum 3-level superradiance Dicke model

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Abstract

It is proved that the quantum 3- level superradiance Dicke model is exactly integrable. The Lax representation of the operator system of evolution equations is derived on the basis of a theory of Lie algebras of currents. The method employed in discussions of the quantum inverse scattering problem is applied to obtain quantum analogs of the action-angle variables. The spectra of the energy operator and of other quantum motion integrals as well as the exact one- and multiparticle excitation eigenstates of the model are constructed. It is shown that the model possesses states of constrained quasiparticles (quantum solitons) that induce superradiance pulses.

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References

  1. A. V. Andreev, V. I. Yemelyanov, and Yu. A. Ilyinskii, “Collective spontaneous radiation (Dicke superradiance),” Usp. Fiz. Nauk,131, 653–687 (1980).

    Google Scholar 

  2. M. M. Bogolyubov, Jr. and A. S. Shumovskii, Superradiance [in Russian], JINS, p-I7-87-176, Dubna (1987), 85 pp.

  3. G. L. I. Lamb, M. O. Scully, and F. A. Hopf, “Higher conservation laws for coherent optical pulse propagation in an inhomogeneously broadened medium,” Appl. Optics,11, No. 11, 2572–2775 (1972).

    Google Scholar 

  4. V. I. Rupasov, “Toward a Dicke superradiance theory. Exact solution of the quasi-one-dimensional quantum model,” Zh. Éksper. Teoret. Fiz.,83, No. 5, 1711–1723 (1987).

    Google Scholar 

  5. N. Yu. Reshetikhin and L. D. Faddeev, “Hamiltonian structure for integrable field theory models,” Teoret. Mat. Fiz.,56, No. 3, 323–343 (1983).

    Google Scholar 

  6. L. D. Faddeev, Quantum Completely Integral Models of Field Theory [in Russian], LDMI, p-2-79, Leningrad (1979), 57 pp.

    Google Scholar 

  7. H. B. Thaker, “Exact integrability in quantum field theory,” Rev. Mod. Phys.,53, 253–279 (1982).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Problems of Mechanics and Mathematics, Academy of Sciences of Ukraine, Lvov

    R. V. Samulyak

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  1. R. V. Samulyak
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Published in Ukrayins'kyy Matematychnyy Zhurnal, Vol. 44, No. 9, pp. 1256–1264, September, 1992.

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Samulyak, R.V. Hamiltonian analysis of exact integrability of the quantum 3-level superradiance Dicke model. Ukr Math J 44, 1149–1155 (1992). https://doi.org/10.1007/BF01058377

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  • DOI: https://doi.org/10.1007/BF01058377

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