›› 2014, Vol. 23 ›› Issue (11): 110302-110302.doi: 10.1088/1674-1056/23/11/110302

• GENERAL • 上一篇    下一篇

Localization and recurrence of a quantum walk in a periodic potential on a line

鄒忠毅a, 何俊麟b   

  1. a Department of Physics, Chinese Culture University, Taipei 111, Taiwan, China;
    b Department of Physics, Tamkang University, Tamsui 251, Taiwan, China
  • 收稿日期:2014-04-25 修回日期:2014-07-02 出版日期:2014-11-15 发布日期:2014-11-15
  • 基金资助:
    Project supported by the Ministry of Science and Technology of Taiwan, China (Grant Nos. NSC-99-2112-M-032-002-MY3 and NSC 102-2112-M-032-003-MY3) and the National Center for Theoretical Sciences (North) (NCTS-n) of China.

Localization and recurrence of a quantum walk in a periodic potential on a line

Chou Chung-I (鄒忠毅)a, Ho Choon-Lin (何俊麟)b   

  1. a Department of Physics, Chinese Culture University, Taipei 111, Taiwan, China;
    b Department of Physics, Tamkang University, Tamsui 251, Taiwan, China
  • Received:2014-04-25 Revised:2014-07-02 Online:2014-11-15 Published:2014-11-15
  • Contact: Ho Choon-Lin E-mail:hcl@mail.tku.edu.tw
  • Supported by:
    Project supported by the Ministry of Science and Technology of Taiwan, China (Grant Nos. NSC-99-2112-M-032-002-MY3 and NSC 102-2112-M-032-003-MY3) and the National Center for Theoretical Sciences (North) (NCTS-n) of China.

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摘要： We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker's coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.

关键词: quantum walk, periodic potential, localization, recurrence

Abstract: We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker's coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.

Key words: quantum walk, periodic potential, localization, recurrence

中图分类号:  (Quantum mechanics)

  • 03.65.-w
03.67.-a (Quantum information) 05.40.Fb (Random walks and Levy flights)