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As is well known, the evolution of quantum state can be replaced by its Wigner function’s time evolution. The Wigner function of a quantum state is the same as the density matrix of a quantum state, because they both contain many messages, such as the probability distribution and phases. Thus, the important information about the quantum state in the evolution process can be obtained more quickly and effectively by studying the Wigner function of a quantum state. In this paper, based on the classical diffusion equation, the diffusion equation of the quantum state density operator is derived by using the P representation of the density operator. Furthermore, by introducing the Weyl ordering symbol of the quantum operator, the corresponding Weyl quantization scheme is given. In addition, the evolution equation of Wigner operator in diffusion channel is established by using another phase space representation of density operator—Wigner function, and the solution form of Wigner operator is given. In this paper, we derive the evolution law of Wigner operator in quantum diffusion channel for the first time, that is, the form of Wigner operator at any time in the evolution process. Based on this conclusion, the evolution of coherent states through quantum diffusion channels is discussed.
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Keywords:
- Wigner function /
- Weyl ordering /
- quantum diffusion channel /
- evolution law
[1] Chakrabarti R, Yogesh V 2018 Physica A 490 886
Google Scholar
[2] Wei C P, Xie F S, Zhang H L, Hu L Y 2013 Int. J. Theor. Phys. 52 798
Google Scholar
[3] Agarwal G S 1971 Phys. Rev. A 3 828
Google Scholar
[4] Hu L Y, Fan H Y 2009 Opt. Commun. 282 4379
Google Scholar
[5] Takahashi K 1986 J. Phys. Soc. Jpn. 55 762
Google Scholar
[6] Fan H Y 1991 Phys. Lett. A 161 1
Google Scholar
[7] Meng X G, Wang J S, Liang B L 2009 Chin. Phys. B 18 01534
Google Scholar
[8] Fan H Y 2010 Commun. Theor. Phys. 53 344
Google Scholar
[9] Fan H Y, Hu L Y 2009 Commun. Theor. Phys. 51 729
Google Scholar
[10] Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
Google Scholar
[11] Kurchan J, Leboeuf P, Saraceno M 1989 Phys. Rev. A 40 6800
Google Scholar
[12] Fan H Y, Zaidi H R 1987 Phys. Lett. A 124 303
Google Scholar
[13] Fan H Y, Wang J S 2007 Commun. Theor. Phys. 47 431
Google Scholar
[14] Fan H Y, Fan Y 1997 Commun. Theor. Phys. 27 105
Google Scholar
[15] 颜森林 2007 物理学报 56 1994
Google Scholar
Yan S L 2007 Acta Phys. Sin. 56 1994
Google Scholar
[16] 兰豆豆, 郭晓敏, 彭春生, 姬玉林, 刘香莲, 李璞, 郭龑强 2017 物理学报 66 120502
Google Scholar
Lan D D, Guo X M, Peng C S, Ji Y L, Liu X L, Li P, Guo Y Q 2017 Acta Phys. Sin. 66 120502
Google Scholar
[17] Weinbub J, Ferry D K 2018 Appl. Phys. Rev. 5 041104
Google Scholar
[18] 范洪义, 梁祖峰 2015 物理学报 64 050301
Google Scholar
Fan H Y, Liang Z F 2015 Acta Phys. Sin. 64 050301
Google Scholar
[19] Wigner E P 1932 Phys. Rev. 40 749
Google Scholar
[20] Fan H Y 1992 J. Phys. A 25 3443
Google Scholar
[21] 袁洪春, 徐学翔 2012 物理学报 61 064205
Google Scholar
Yuan H C, Xu X X 2012 Acta Phys. Sin. 61 064205
Google Scholar
[22] Fan H Y, Yang Y L 2006 Phys. Lett. A 353 439
Google Scholar
[23] Zhang K, Fan C Y, Fan H Y 2019 Int. J. Theor. Phys. 58 1687
Google Scholar
[24] Buot F, Jensen K 1990 Phys. Rev. B 42 9429
Google Scholar
[25] Chountasis S, Vourdas A 1998 Phys. Rev. A 58 1794
Google Scholar
[26] Fan H Y, Hu L Y, Yuan H C 2010 Chin. Phys. B 19 060305
Google Scholar
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图 1 (a)
$kt = 0$ , (b)$kt = 0.8$ 时, 相干态下Wigner算符的演化规律($\alpha = 1/2\left( {1 + i} \right)$ )Figure 1. Evolution law of Wigner operator for the coherent state with
$\alpha = 1/2\left( {1 + i} \right)$ for (a)$kt = 0$ ; (b)$kt = 0.8$ -
[1] Chakrabarti R, Yogesh V 2018 Physica A 490 886
Google Scholar
[2] Wei C P, Xie F S, Zhang H L, Hu L Y 2013 Int. J. Theor. Phys. 52 798
Google Scholar
[3] Agarwal G S 1971 Phys. Rev. A 3 828
Google Scholar
[4] Hu L Y, Fan H Y 2009 Opt. Commun. 282 4379
Google Scholar
[5] Takahashi K 1986 J. Phys. Soc. Jpn. 55 762
Google Scholar
[6] Fan H Y 1991 Phys. Lett. A 161 1
Google Scholar
[7] Meng X G, Wang J S, Liang B L 2009 Chin. Phys. B 18 01534
Google Scholar
[8] Fan H Y 2010 Commun. Theor. Phys. 53 344
Google Scholar
[9] Fan H Y, Hu L Y 2009 Commun. Theor. Phys. 51 729
Google Scholar
[10] Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
Google Scholar
[11] Kurchan J, Leboeuf P, Saraceno M 1989 Phys. Rev. A 40 6800
Google Scholar
[12] Fan H Y, Zaidi H R 1987 Phys. Lett. A 124 303
Google Scholar
[13] Fan H Y, Wang J S 2007 Commun. Theor. Phys. 47 431
Google Scholar
[14] Fan H Y, Fan Y 1997 Commun. Theor. Phys. 27 105
Google Scholar
[15] 颜森林 2007 物理学报 56 1994
Google Scholar
Yan S L 2007 Acta Phys. Sin. 56 1994
Google Scholar
[16] 兰豆豆, 郭晓敏, 彭春生, 姬玉林, 刘香莲, 李璞, 郭龑强 2017 物理学报 66 120502
Google Scholar
Lan D D, Guo X M, Peng C S, Ji Y L, Liu X L, Li P, Guo Y Q 2017 Acta Phys. Sin. 66 120502
Google Scholar
[17] Weinbub J, Ferry D K 2018 Appl. Phys. Rev. 5 041104
Google Scholar
[18] 范洪义, 梁祖峰 2015 物理学报 64 050301
Google Scholar
Fan H Y, Liang Z F 2015 Acta Phys. Sin. 64 050301
Google Scholar
[19] Wigner E P 1932 Phys. Rev. 40 749
Google Scholar
[20] Fan H Y 1992 J. Phys. A 25 3443
Google Scholar
[21] 袁洪春, 徐学翔 2012 物理学报 61 064205
Google Scholar
Yuan H C, Xu X X 2012 Acta Phys. Sin. 61 064205
Google Scholar
[22] Fan H Y, Yang Y L 2006 Phys. Lett. A 353 439
Google Scholar
[23] Zhang K, Fan C Y, Fan H Y 2019 Int. J. Theor. Phys. 58 1687
Google Scholar
[24] Buot F, Jensen K 1990 Phys. Rev. B 42 9429
Google Scholar
[25] Chountasis S, Vourdas A 1998 Phys. Rev. A 58 1794
Google Scholar
[26] Fan H Y, Hu L Y, Yuan H C 2010 Chin. Phys. B 19 060305
Google Scholar
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