Acta Physica Sinica, Volume. 69, Issue 9, 090301-1(2020)

Time evolution law of Wigner operator in diffusion channel

Ke Zhang1, Lan-Lan Li1, Gang Ren1, Jian-Ming Du1, and Hong-Yi Fan2、*
Author Affiliations
  • 1School of Electronic Engineering, Huainan Normal University, Huainan 232038, China
  • 2Science Island Branch of Graduate School, University of Science and Technology of China, Hefei 230031, China
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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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    Ke Zhang, Lan-Lan Li, Gang Ren, Jian-Ming Du, Hong-Yi Fan. Time evolution law of Wigner operator in diffusion channel[J]. Acta Physica Sinica, 2020, 69(9): 090301-1

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    Paper Information

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    Received: Jan. 15, 2020

    Accepted: --

    Published Online: Nov. 26, 2020

    The Author Email:

    DOI:10.7498/aps.69.20200106

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