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Wave packet dynamics, ergodicity, and localization in quasiperiodic chains

Thiem, Stefanie; Schreiber, Michael and Grimm, Uwe (2009). Wave packet dynamics, ergodicity, and localization in quasiperiodic chains. Physical Review B, 80(21) p. 214203.

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In this paper, we report results for the wave packet dynamics in a class of quasiperiodic chains consisting of two types of weakly coupled clusters. The dynamics are studied by means of the return probability and the mean-square displacement. The wave packets show anomalous diffusion in a stepwise process of fast expansion followed by time intervals of confined wave packet width. Applying perturbation theory, where the coupling parameter v is treated as perturbation, the properties of the eigenstates of the system are investigated and related to the structure of the chains. The results show the appearance of nonlocalized states only in sufficiently high orders of the perturbation expansions. Further, we compare these results to the exact solutions obtained by numerical diagonalization. This shows that eigenstates spread across the entire chain for v>0, while in the limit v->0 ergodicity is broken and eigenstates only spread across clusters of the same type, in contradistinction to trivial localization for v=0. Caused by this ergodicity breaking, the wave packet dynamics change significantly in the presence of an impurity offering the possibility to control its long-term dynamics.

Item Type: Journal Item
Copyright Holders: 2009 The American Physical Society
ISSN: 1098-0121
Project Funding Details:
Funded Project NameProject IDFunding Body
Combinatorics of Sequences and Tilings and its ApplicationsEP/D058465/1EPSRC (Engineering and Physical Sciences Research Council)
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM)
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Item ID: 19420
Depositing User: Uwe Grimm
Date Deposited: 06 Jan 2010 12:13
Last Modified: 07 Dec 2018 09:30
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