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Parametric interactions and scattering

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Abstract

We show how a variety of parametric Hamiltonians arise by a limiting procedure applied to a time-independent Hamiltonian. We then study one such Hamiltonian, that for a parametric frequency converter, in detail and find its associated Raman scattering matrix.

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References

  1. Dicke, R. H.: Coherence in spontaneous radiation processes. Phys. Rev.93, 99–110 (1954)

    Google Scholar 

  2. Scharf, G.: On a quantum mechanical maser model. Helv. Phys. Acta43, 806–828 (1970)

    Google Scholar 

  3. Bonifacio, R., Preparata, G.: Coherent spontaneous emission. Phys. Rev.2A, 336–347 (1970)

    Google Scholar 

  4. Hepp, K., Lieb, E. H.: On the superradiant phase transition for molecules in a quantised radiation field: the Dieke maser model. Ann. Phys.76, 360–404 (1973)

    Google Scholar 

  5. Hepp, K., Lieb, E. H.: Phase transitions in reservoir driven open systems with applications to lasers and superconductors. Helv. Phys. Acta46, 573–603 (1973)

    Google Scholar 

  6. Hepp, K., Lieb, E. H.: The equilibrium statistical mechanics of matter interacting with the quantised radiation field. Phys. Rev. A8, 2517–2525 (1973)

    Google Scholar 

  7. Wang, Y. K., Hioe, F. T.: Phase transition in the Dicke model of superradiance. Phys. Rev.7A, 831–836 (1973)

    Google Scholar 

  8. Hioe, F. T.: Phase transitions in some generalised Dicke models of superradiance. (To appear)

  9. Davies, E. B.: Exact dynamics of an infinite atom Dicke maser model. Commun. math. Phys.33, 187–205 (1973)

    Google Scholar 

  10. Davies, E. B.: The infinite atom Dicke maser model II. Commun. math. Phys.34, 237–249 (1973)

    Google Scholar 

  11. Louisell, W. H., Yariv, A., Siegman, A. E.: Quantum fluctuations and noise in parametric processes I. Phys. Rev.124, 1646–1654 (1961)

    Google Scholar 

  12. Louisell, W.: Radiation and noise in quantum electronics. New York: McGraw Hill 1964

    Google Scholar 

  13. Kato, T.: Perturbation theory for linear operators. New York: Springer 1966

    Google Scholar 

  14. Shale, D., Stinespring, W. F.: A note on the scattering of Boson fields. J. Math. Phys.3, 915–921 (1962)

    Google Scholar 

  15. Davies, E. B.: Quantum stochastic processes. Commun. math. Phys.15, 277–304 (1969)

    Google Scholar 

  16. Serber, R., Townes, C. H.: In: Townes, C. H. (Ed.): Quantum electronics. New York: Columbia Univ. Press 1960

    Google Scholar 

  17. Mollow, B. R., Glauber, R. J.: Quantum theory of parametric amplification I and II. Phys. Rev.160, 1076–1096, 1097–1108 (1967)

    Google Scholar 

  18. Lu, E. Y. C.: New coherent states for the electromagnetic field. Lett. Nuovo Cimento2, 1241–1244 (1971)

    Google Scholar 

  19. Lu, E. Y. C.: Quantum correlations in two-photon amplification. Lett. Nuovo Cimento3, 585–589 (1972)

    Google Scholar 

  20. Perelomov, A. M.: Coherent states for arbitrary Lie groups. Commun. math. Phys.26, 222–236 (1972)

    Google Scholar 

  21. Phillips, R. S.: Perturbation theory for semi-groups of linear operators. Trans. Amer. Math. Soc.74, 199–221 (1954)

    Google Scholar 

  22. Kisynski, J.: Sur les operateurs de Green des problemes de Cauchy abstraits. Studia Math.23, 285–328 (1964)

    Google Scholar 

  23. Yosida, K.: Functional analysis. New York: Springer 1965

    Google Scholar 

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Authors and Affiliations

  1. Mathematical Institute, Oxford, U.K.

    E. B. Davies

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  1. E. B. Davies
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Communicated by K. Hepp

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Davies, E.B. Parametric interactions and scattering. Commun.Math. Phys. 37, 161–174 (1974). https://doi.org/10.1007/BF01646208

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  • DOI: https://doi.org/10.1007/BF01646208

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