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.
Received: 08 June 2007
Revised: 30 July 2007
Accepted manuscript online:
Fund: 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.
Cite this article:
Zhang Kai-Wang(张凯旺) Quantum diffusion in semi-infinite periodic and quasiperiodic systems 2008 Chin. Phys. B 17 1113
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