ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
Prev
Next
|
|
|
A generalized Weyl–Wigner quantization scheme unifying P–Q and Q–P ordering and Weyl ordering of operators |
Wang Ji-Suo(王继锁)a)b)†, Fan Hong-Yi(范洪义) c), and Meng Xiang-Guo(孟祥国)b)c) |
a. Shandong Provincial Key Laboratory of Laser Polarization and Information Technology,College of Physics and Engineering, Qufu Normal University, Qufu 273165, China;
b. Department of Physics, Liaocheng University, Liaocheng 252059, China;
c. Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China |
|
|
Abstract By extending the usual Wigner operator to the s-parameterized one as (1/4π2)∫-∞∞ dyduexp≤[iu≤(q-Q) + iy≤(p-P) + i(s/2)yu] with s being a real parameter, we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule. This rule recovers P-Q ordering, Q-P ordering, and Weyl ordering of operators in s=1,-1,0 respectively. Hence it differs from the Cahill-Glaubers' ordering rule which unifies normal ordering, anti-normal ordering, and Weyl ordering. We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P. The formula that can rearrange a given operator into its new s-parameterized ordering is presented.
|
Received: 18 November 2011
Revised: 10 December 2011
Accepted manuscript online:
|
PACS:
|
42.50.-p
|
(Quantum optics)
|
|
03.65.-w
|
(Quantum mechanics)
|
|
05.30.-d
|
(Quantum statistical mechanics)
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11147009), the Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AQ027), and the Program of Higher Educational Science and Technology of Shandong Province, China (Grant No. J10LA15). |
Corresponding Authors:
Wang Ji-Suo
E-mail: jswang@qfnu.edu.cn
|
Cite this article:
Wang Ji-Suo(王继锁), Fan Hong-Yi(范洪义), and Meng Xiang-Guo(孟祥国) A generalized Weyl–Wigner quantization scheme unifying P–Q and Q–P ordering and Weyl ordering of operators 2012 Chin. Phys. B 21 064204
|
[1] |
See e.g., Schleich W P 2001 Quantum Optics in Phase Space (Berlin: Wiley-VCH)
|
[2] |
Torres-Vega G and Frederick J H 1990 J. Chem. Phys. 93 8862
|
[3] |
Agarwal G S and Wolf E 1970 Phys. Rev. D 2 2161
|
[4] |
Hu L Y and Fan H Y 2009 Phys. Rev. A 80 022115
|
[5] |
Wigner E 1932 Phys. Rev. 40 749
|
[6] |
Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R147
|
[7] |
Fan H Y and Zaidi H 1987 Phys. Lett. A 124 303
|
[8] |
Weyl H 1927 Z. Phys. 46 1
|
[9] |
Fan H Y 1992 J. Phys. A: Math. Gen. 25 3443
|
[10] |
Cohen L 1966 J. Math. Phys. 7 781
|
[11] |
Cahill K E and Glauber R J 1969 Phys. Rev. 177 1857
|
[12] |
Glauber R J 1963 Phys. Rev. 131 2766
|
[13] |
Mehta C L 1967 Phys. Rev. Lett. 18 752
|
[14] |
Wang J S, Meng X G and Liang B L 2010 Chin. Phys. B 19 014207
|
[15] |
Meng X G, Wang J S and Liang B L 2011 Chin. Phys. B 20 014204
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|