中国物理B ›› 2008, Vol. 17 ›› Issue (3): 1113-1118.doi: 10.1088/1674-1056/17/3/060

• CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES • 上一篇    下一篇

Quantum diffusion in semi-infinite periodic and quasiperiodic systems

张凯旺   

  1. Department of Physics, Xiangtan University, Hunan rm 411105, China
  • 收稿日期:2007-06-08 修回日期:2007-07-30 出版日期:2008-03-04 发布日期:2008-03-04
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 19674046), by the Cheung Kong Scholars Programme of China, and by the Construct Program of the Key Discipline in Hunan Province, China.

Quantum diffusion in semi-infinite periodic and quasiperiodic systems

Zhang Kai-Wang(张凯旺)†   

  1. Department of Physics, Xiangtan University, Hunan rm 411105, China
  • Received:2007-06-08 Revised:2007-07-30 Online:2008-03-04 Published:2008-03-04
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 19674046), by the Cheung Kong Scholars Programme of China, and by the Construct Program of the Key Discipline in Hunan Province, China.

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摘要： This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still $C(t)\sim t^{ - \delta }$ and $d(t)\sim t^{\beta }$. However, it finds that $0 < \delta < 1$ for smaller time, and $\delta = 0$ for larger time due to the influence of surface localized states. Moreover, $\beta $ for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.

Abstract: This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still $C(t)\sim t^{ - \delta }$ and $d(t)\sim t^{\beta }$. However, it finds that $0 < \delta < 1$ for smaller time, and $\delta = 0$ for larger time due to the influence of surface localized states. Moreover, $\beta $ for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.

Key words: quantum diffusion, semi-infinite, periodic lattice, quasiperiodic Fibonacci lattice

中图分类号:  (Quasicrystals)

  • 71.23.Ft
68.35.Fx (Diffusion; interface formation) 71.23.An (Theories and models; localized states) 73.20.Fz (Weak or Anderson localization)