A multifractal study of wave functions in 1-D quasicrystals

Ananthakrishna, G. ; Kumar, Vijay (1991) A multifractal study of wave functions in 1-D quasicrystals Pramana - Journal of Physics, 36 (3). pp. 335-346. ISSN 0304-4289

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Official URL: http://www.ias.ac.in/j_archive/pramana/36/3/335-34...

Related URL: http://dx.doi.org/10.1007/BF02846553


Using multifractal analysis we study extended, self-similar and non-self-similar type of wave functions in the Fibonacci model. Extended states arising due to commutation of transfer matrices for certain blocks of atoms in quasiperiodic systems are shown to have the same signature as the Bloch states in terms of the singularity spectrum with f(α )=α =1. Numerically, however, the extended states show a typical multifractal behaviour for finite chain lengths. Finite size scaling corrections yield results consistent with that obtained analytically. The self-similar states at the band edges show a multifractal behaviour and they are energy dependent in the case of blocks of atoms arranged in a Fibonacci sequence. For non-self-similar states we obtain a non-monotonic behaviour off(α ) as a function of the chain length. We also show that in cases where extended states exist, the cross-over from extended to non-self-similar states in gradual.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Multifractal; Signularity Spectrum; Self-similar Wave Functions; Quasicrystal; Fibonacci Chain
ID Code:72014
Deposited On:28 Nov 2011 05:14
Last Modified:18 May 2016 17:27

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