Berlin 2005 – wissenschaftliches Programm
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M: Metallphysik
M 27: Quasikristalle
M 27.3: Vortrag
Montag, 7. März 2005, 11:00–11:15, TU H111
Multiscaling, Ergodicity and Localization in Quasiperiodic Chains — •V. Z. Cerovski1, M. Schreiber1, and U. Grimm2 — 1Institute für Physik, Technische Universität Chemnitz, D-09107 Chemnitz — 2The Open University, Applied Mathematics Dept., Milton Keynes, MK76AA, UK.
We report results of numerical simulations of wavepacket dynamics in a class of chains consisting of two types of weakly coupled clusters arranged in a quasiperiodic sequence and investigate properties of eigenstates using the perturbation theory of degenerate levels in the coupling strength v and numerical diagonalization. Results show that wave packets anomalously diffuse via a two-step process of rapid and slow expansions, that persist for any v>0. An elementary analysis of the perturbation theory of degenerate levels reveal that non-localized states appear only in sufficiently high order of perturbation theory that is simply related to the combinatorial properties of the sequences, and numerical diagonalization furthermore shows that eigenstates ergodically spread across the whole chain for v>0, while in the limit v→ 0 ergodicity is broken and eigenstates spread only across clusters with the same number of atoms, in contradistinction with trivial localization at v=0. Effects of the single-site perturbation on wavepacket dynamics are furthermore investigated and shown that by changing the position or strength of the impurity it is possible to control long-time wavepacket dynamics. By adding a single impurity it is possible to induce wavepacket localization on individual subchains as well as on the whole chain.