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Ten Years of the Positive P-Representation

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Recent Developments in Quantum Optics

Abstract

The positive P-representation is an example of a new class of phase-space representations, which utilize a nonclassical phase-space. These have many applications, and have been widely used in quantum optics in the last decade, since their introduction. The utility of the positive P-representation is that it retains many of the advantages of the diagonal P-representation, while still remaining nonsingular, even for nonlinear Hamiltonians. However, attention to boundary terms and to the use of stable integration methods are important.

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References

  1. J. von Neumann: Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton 1955).

    MATH  Google Scholar 

  2. E. P. Wigner: Phys. Rev. 40, 749 (1932).

    Article  MATH  Google Scholar 

  3. R. J. Glauber: Phys. Rev. 131, 2766 (1963); E. C. G. Sudarshan: Phys. Rev. Lett. 10, 277 (1963).

    Article  MathSciNet  Google Scholar 

  4. J. R. Klauder, J. McKenna, D. G. Currie: J. Math. Phys. 6, 734 (1965).

    Article  MATH  MathSciNet  Google Scholar 

  5. C. W. Gardiner: Handbook of Stochastic Methods (2nd ed.) (Springer, Heidelberg 1985, 1990).

    Google Scholar 

  6. P. D. Drummond, C. W. Gardiner: J. Phys. A13, 2353 (1980).

    Article  MathSciNet  Google Scholar 

  7. C. W. Gardiner: Quantum Noise (Springer, Heidelberg 1991).

    MATH  Google Scholar 

  8. M. Wolinsky, H. J. Carmichael: Phys. Rev. Lett. 60, 1836 (1988).

    Article  Google Scholar 

  9. P. Kinsler, P. D. Drummond: Phys. Rev. Lett. 64, 236 (1990); P. D. Drummond, P. Kinsler: Phys. Rev. A40, 4813 (1989).

    Article  Google Scholar 

  10. A. M. Smith, C. W. Gardiner: Phys. Rev. A39, 3511 (1989).

    Article  Google Scholar 

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© 1993 Plenum Press, New York

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Gardiner, C.W., Drummond, P.D. (1993). Ten Years of the Positive P-Representation. In: Inguva, R. (eds) Recent Developments in Quantum Optics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2936-1_9

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  • DOI: https://doi.org/10.1007/978-1-4615-2936-1_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-44403-6

  • Online ISBN: 978-1-4615-2936-1

  • eBook Packages: Springer Book Archive

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