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What determines the spreading of a wave packet?

R. Ketzmerick·K. Kruse·S. Kraut·T. Geisel
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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.

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R. Ketzmerick, K. Kruse, S. Kraut, T. Geisel. 1997-08-19. What determines the spreading of a wave packet?. https://doi.org/10.1103/physrevlett.79.1959

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