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Exactly solvable models of quantum nonlinear optics

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There are many models in quantum nonlinear optics that are exactly solvable and allow one to describe physical phenomena beyond perturbation theory. We show that many such models can be solved in the framework of the quantum inverse scattering method. Bibliography: 34 titles.

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References

  1. L. D. Faddeev and L. A. Takhtajan, Usp. Mat. Nauk, 34, 13 (1979).

    Google Scholar 

  2. E. K. Sklyanin, L. A. Takhtajan, and L. D. Faddeev, Teor. Mat. Fiz., 40, 194 (1979).

    Article  Google Scholar 

  3. L. D. Faddeev, “Quantum completely integrable models of field theory,” Sov. Sci. Rev. Math. C., 1, 107–160 (1980).

    MATH  Google Scholar 

  4. P. P. Kulish and E. K. Sklyanin, “Quantum spectral transform method. Recent developments,” Lent. Notes Phys., 151, 61–119 (1982).

    Article  MathSciNet  Google Scholar 

  5. V. E. Korepin, N. M. Bogoliubov, and A. G. lzergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Univ. Press, Cambridge (1993).

  6. E. T. Jaynes and F. W. Cummings, Proc. IEEE, 51, 89 (1963).

    Article  Google Scholar 

  7. I. Rabi, Phys. Rev., 49, 324 (1936).

    Article  MATH  Google Scholar 

  8. D. Braak, Phys. Rev., 107, 100401 (2011).

    Google Scholar 

  9. M. Tavis and F. W. Cummings, Phys. Rev., 170, 379 (1968).

    Article  Google Scholar 

  10. M. Gaudin, La Fonction D’onde de Bethe, Masson, Paris (1983).

    MATH  Google Scholar 

  11. R. W. Richardson, J. Math. Phys., 9, 1327 (1968).

    Article  Google Scholar 

  12. L. Amico, A. Di Lorenzo, and A. Osterloh, Nucl. Phys. B, 614, 449 (2001).

    Article  MATH  Google Scholar 

  13. M. Chaichian, D. Ellinas, and P. P. Kulish, Phys. Rev. Lett., 65, 980 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  14. P. P. Kulish and E. V. Damaskinsky, J. Phys. A, 23, L415 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  15. O. Babelon and D. Talalaev, J. Stat. Mech., 0706:P06013 (2007).

    Google Scholar 

  16. M. O. Scully and M. S. Zubairy, Quantum Optics, Cambridge Univ. Press, Cambridge (1997).

    Book  Google Scholar 

  17. R. H. Dicke, Phys. Rev., 93, 99 (1954).

    Article  MATH  Google Scholar 

  18. V. N. Popov and V. S. Yarunin, Collective Effects in Quantum Statistics of Radiation and Matter, Kluwer, Dordrecht (1988).

    Book  Google Scholar 

  19. N. M. Bogoliubov, R. K. Bullough, and J. Timonen, J. Phys. A, 29, 6305 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  20. V. I. Rupasov and V. I. Yudson, Sov. Phys. JETP, 59, 478 (1984).

    MathSciNet  Google Scholar 

  21. E. Lieb and W. Liniger, Phys. Rev., 130, 1605 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  22. W. Ketterle, The Nobel Prizes 2001, Stockholm (2002).

  23. N. N. Bogoliubov, Izv. Ahad. Nauh SSSR, Ser. Fiz., 11, 77 (1947).

    Google Scholar 

  24. J. Dukelsky and P. Schuck, Phys. Rev. Lett., 86, 4206 (2001).

    Google Scholar 

  25. S. E. Pollack et al., Phys. Rev. Lett., 102, 090402 (2009).

    Article  Google Scholar 

  26. E. Haller et al., Science, 325, 1224 (2009).

    Article  Google Scholar 

  27. P. P. Kulish, Lett. Math. Phys., 5, 191 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  28. V. S. Gerdjikov, M. Ivanov, and P. P. Kulish, J. Math. Phys., 25, 25 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  29. N. M. Bogoliubov, R. K. Bullough, and G. D. Pang, Phys. Rev. B, 47, 11495 (1993).

    Article  Google Scholar 

  30. N. M. Bogoliubov, R. K. Bullough, and J. Timonen. Phys. Rev. Lett., 72. 3933 (1994).

    Google Scholar 

  31. N. M. Bogoliubov, A. G. lzergin. and N. A, Kitanine, Nucl. Phys. B. 516, 501 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  32. N. Bogoliubov and J. Timonen, Philos. Transact. A, 369, 1319 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  33. N. M. Bogoliubov, A. V. Rybin, and J. Timonen, J. Phys. A, 27, L363 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  34. I. G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford (1995).

    MATH  Google Scholar 

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Correspondence to N. M. Bogoliubov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 398, 2012, pp. 26–54.

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Bogoliubov, N.M., Kulish, P.P. Exactly solvable models of quantum nonlinear optics. J Math Sci 192, 14–30 (2013). https://doi.org/10.1007/s10958-013-1369-7

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  • DOI: https://doi.org/10.1007/s10958-013-1369-7

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