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Rigorous solution to a quantum statistical mechanical laser model

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  • Shibata, Fumiaki
  • Uchiyama, Chikako

Abstract

A quantum mechanical laser model with relaxation and pumping mechanisms is solved rigorously. A basic equation for the density matrix is derived by the damping theory and is transformed into a corresponding c-number equation for a (quasi-) probability density. This is done with the aid of the quantum phase space method. The probability density is expanded in terms of orthogonal polynomials. The expansion coefficients are solved to give a continued fraction. A complete solution is obtained, namely, time evolution of the probability density is determined as well as that for certain physical quantities. The solution is valid even for strong coupling between photons and atoms: it is free from restriction on system parameters. Detailed studies on dynamics are performed for typical values of the system parameters. This is a prototype of interacting quantum nonequilibrium systems. Relevance to systems other than a laser is briefly mentioned.

Suggested Citation

  • Shibata, Fumiaki & Uchiyama, Chikako, 1995. "Rigorous solution to a quantum statistical mechanical laser model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(2), pages 242-276.
    • Handle: RePEc:eee:phsmap:v:214:y:1995:i:2:p:242-276
    DOI: 10.1016/0378-4371(94)00218-I
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    1. Kirchner, Walther, 1985. "Modern Europe - The Interactions of Amsterdam and Antwerp with the Baltic Region, 1400–1800/De Nederlanden en her Oostzeegebied, 1400–1800. Prepared by Nederlandsch Economisch-Historisch Archief. Pape," The Journal of Economic History, Cambridge University Press, vol. 45(2), pages 484-485, June.
    2. Uchiyama, Chikako & Shibata, Fumiaki, 1993. "A path integral theory of relaxation II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 198(3), pages 538-550.
    3. Ketterer, Karl-Heinz & Vollmer, Rainer, 1980. "Sozio-ökonomische Aspekte der Geldwertentwicklung," Wirtschaftsdienst – Zeitschrift für Wirtschaftspolitik (1949 - 2007), ZBW - Leibniz Information Centre for Economics, vol. 60(8), pages 407-412.
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    Cited by:

    1. Uspenskii, Yu.A. & Kulatov, E.T. & Halilov, S.V., 1997. "Ab initio studies of optical and magneto-optical spectra in 3d- and 4f-atom-based compounds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(1), pages 89-93.
    2. Panina, L.V. & Mohri, K. & Uchiyama, T., 1997. "Giant magneto-impedance (GMI) in amorphous wire, single layer film and sandwich film," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(1), pages 429-438.

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