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Wave Kinetic Approach

  • J. T. Mendonça
  • Hugo Terças
Chapter
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 70)

Abstract

Here we give an introductory account of the wave kinetic theory. Its basic ingredients are the Wigner function and its evolution equation. Historically it started in 1932, when Wigner proposed his function as a way to represent the quantum state of a particle in its classical phase space [1]. Later, in 1949, Moyal was ableto derive an exact evolution equation for the Wigner function, starting from the Shrödinger equation [2]. In the classical limit, this evolution equation tends to the classical single particle Liouville equation. With these two pieces of knowledge, we are able today to build-up a consistent description of quantum particles in self consistent mean-fields, which are very useful to describe many different processes in quantum gases, namely, elementary excitations, collective processes and resonant interactions, as shown through many different examples in this book. This wave kinetic description has been abundantly used in the literature, and in particular for laser cooling, as discussed in the reviews [3, 4].

Keywords

Wigner Function Laser Field Density Matrix Element Weyl Transformation Classical Phase Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    E.P. Wigner, Phys. Rev. 40, 749 (1932)ADSCrossRefGoogle Scholar
  2. 2.
    J.E. Moyal, Proc. Camb. Philos. Soc. 45, 99 (1949)MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    S. Stenholm, The semiclassical theory of laser cooling. Rev. Mod. Phys. 58, 699 (1986)ADSCrossRefGoogle Scholar
  4. 4.
    J. Dalibard, C. Cohen-Tannoudji, Atomic motion in laser light: connection between semiclassical and quantum description. J. Phys. B At. Mol. Phys. 18, 1661 (1985)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    M. Hillary, R.F. O’Connell, M.O. Scully, E.P. Wigner, Distribution functions in physics: fundamentals. Phys. Rep. 106, 121 (1984)MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    R. Loudon, The Quantum Theory of Light. Oxford Science Publications (Clarendon, Oxford, 1992)Google Scholar
  7. 7.
    M.O. Scully, M.S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge/New York, 1999)CrossRefGoogle Scholar
  8. 8.
    M. Kasevich, S. Chu, Phys. Rev. Lett. 69, 1741 (1992)ADSCrossRefGoogle Scholar
  9. 9.
    C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge/New York, 2008)CrossRefGoogle Scholar
  10. 10.
    A.E. Kaplan, Opt. Express 17, 10035 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    K. Vahala, M. Herrmann, S. Knunz, V. Batteiger, G. Saathoff, T.W. Hänsch, Th. Udem, Nat. Phys. 5, 682 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • J. T. Mendonça
    • 1
  • Hugo Terças
    • 2
  1. 1.Instituto Superior TecnicoLisbonPortugal
  2. 2.Université Blaise PascalAubière CedexFrance

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