| 量子扩散通道中Wigner算符的演化规律 |
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| 引用本文： | 张科,李兰兰,任刚,杜建明,范洪义.量子扩散通道中Wigner算符的演化规律[J].物理学报,2020(9):41-47. |
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| 作者姓名： | 张科 李兰兰 任刚 杜建明 范洪义 |
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| 作者单位： | 淮南师范学院电子工程学院;中国科学技术大学研究生院科学岛分院 |
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| 基金项目： | 国家自然科学基金(批准号:11775208);安徽省教育厅自然科学重点项目(批准号:KJ2019A0688);淮南师范学院重点研究项目(批准号:2019XJZD04)资助的课题. |
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| 摘 要： | 众所周知,量子态的演化可用与其相应的Wigner函数演化来代替.因为量子态的Wigner函数和量子态的密度矩阵一样,都包含了概率分布和相位等信息,因此对量子态的Wigner函数进行研究,可以更加快速有效地获取量子态在演化过程的重要信息.本文从经典扩散方程出发,利用密度算符的P表示,导出了量子态密度算符的扩散方程.进一步通过引入量子算符的Weyl编序记号,给出了其对应的Weyl量子化方案.另外,借助于密度算符的另一相空间表示-Wigner函数,建立了Wigner算符在扩散通道中演化方程,并给出了其Wigner算符解的形式.本文推导出了Wigner算符在量子扩散通道中的演化规律,即演化过程中任意时刻Wigner算符的形式.在此结论的基础上,讨论了相干态经过量子扩散通道的演化情况.
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| 关 键 词： | WIGNER函数 Weyl编序 量子扩散通道 演化规律 |
Time evolution law of Wigner operator in diffusion channel |
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| Zhang Ke,Li Lan-Lan,Ren Gang,Du Jian-Ming,Fan Hong-Yi.Time evolution law of Wigner operator in diffusion channel[J].Acta Physica Sinica,2020(9):41-47. |
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| Authors: | Zhang Ke Li Lan-Lan Ren Gang Du Jian-Ming Fan Hong-Yi |
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| Affiliation: | (School of Electronic Engineering,Huainan Normal University,Huainan 232038,China;Science Island Branch of Graduate School,University of Science and Technology of China,Hefei 230031,China) |
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| Abstract: | 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 |
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