What determines the spreading of a wave packet?

There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

Abstract

The multifractal dimensions D2^mu and D2^psi of the energy spectrum and eigenfunctions, resp., are shown to determine the asymptotic scaling of the width of a spreading wave packet. For systems where the shape of the wave packet is preserved the k-th moment increases as t^(k*beta) with beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound. Furthermore, we show that in d dimensions asymptotically in time the center of any wave packet decreases spatially as a power law with exponent D_2^psi - d and present numerical support for these results.

Related collections

Most cited references 8

Record: found
Abstract: not found
Article: not found

Scaling, Diffusion, and the Integer Quantized Hall Effect

J. Chalker, G. Daniell (1988)

0 comments Cited 99 times – based on 0 reviews      Review now

Bookmark

Record: found
Abstract: found
Article: found

Is Open Access

Relation between the Correlation Dimensions of Multifractal Wavefunctions and Spectral Measures in Integer Quantum Hall Systems

B. Huckestein, L. Schweitzer (1994)

We study the time evolution of wavepackets of non-interacting electrons in a two-dimensional disordered system in strong magnetic field. For wavepackets built from states near the metal-insulator transition in the center of the lowest Landau band we find that the return probability to the origin \(p(t)\) decays algebraically, \(p(t) \sim t^{-D_2/2}\), with a non-conventional exponent \(D_2/2\). \(D_2\) is the generalized dimension describing the scaling of the second moment of the wavefunction. We show that the corresponding spectral measure is multifractal and that the exponent \(D_2/2\) equals the generalized dimension \(\widetilde{D}_2\) of the spectral measure.