| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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A Family of Generalized Wigner Operators and Their Physical Meaning as Bivariate Normal Distribution |
| WANG Ji-Suo1,2**, MENG Xiang-Guo2, FAN Hong-Yi2
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1Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, College of Physics and Engineering, Qufu Normal University, Qufu 273165
2Department of Physics, Liaocheng University, Liaocheng 252059
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| Cite this article: |
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WANG Ji-Suo, MENG Xiang-Guo, FAN Hong-Yi 2011 Chin. Phys. Lett. 28 104209 |
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Abstract By extending the usual Wigner operator to the s−parameterized one, we find that in the process of the generalized Weyl quantization the s parameter plays the role of correlation between two quadratures Q and P. This can be exposed by comparing the normally ordered form of Ωs with the standard form of the Gaussian bivariate normal distribution of random variables in statistics. Three different expressions of Ωs and the quantization scheme with use of it are presented.
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| Keywords:
42.50.-p
03.65.-w
05.30.-d
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Received: 16 February 2011
Published: 28 September 2011
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[1] Wigner E P 1932 Phys. Rev. A 40 749
[2] Weyl H 1927 Z. Phys. 46 1
[3] Cohen L 1966 J. Math. Phys. 7 781
[4] Schleich W 2001 Quantum Optics in Phase Space (Berlin: Viley-VCH)
[5] Torres-Vega G and Frederick J H 1990 J. Chem. Phys. 93 8862
[6] Agarwal G S and Wolf E 1970 Phys. Rev. D 2 2161
[7] Hu L Y and Fan H Y 2009 Phys. Rev. A 80 022115
Hu L Y, Fan H Y and Lu H L 2008 J. Chem. Phys. 128 054101
[8] Xu Y J, Fan H Y and Liu Q Y 2010 Chin. Phys. B 2 020303
[9] Fan H Y and Zaidi H 1987 Phys. Lett. A 124 303
[10] Hoel P 1966 Elementary Statistics (New York: John Wiley)
[11] Fan H Y 2008 Ann. Phys. 323 1502
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