1996/11/30 by Roland Ketzmerick, R. Ketzmerick, K. Kruse +4 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #BETA (programming language) #Center (category theory) #Computer science #Diffusion and Search Dynamics #Eigenfunction #Eigenvalues and eigenvectors #Energy (signal processing) #Exponent #Geometry #Mathematics #Moment (physics) #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Scaling #Second moment of area #Theoretical and Computational Physics #Wave packet #chao-dyn #cond-mat.mes-hall #nlin.CD
paper · pdf · doi:10.1103/physrevlett.79.1959
published as Phys. Rev. Lett. 79 (1997) 1959 · Physical Review Letters to appear, 4 pages postscript with figures
arxiv created 1997/08/19 · openalex publication_date 1997/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The multifractal dimensions D2^\ensuremathμ and D2^\ensuremathψ of the energy spectrum and eigenfunctions, respectively, 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 kth moment increases as t^k\ensuremathβ with \ensuremathβ\phantom\rule0ex0ex=\phantom\rule0ex0exD2^\ensuremathμ/D2^\ensuremathψ, while, in general, t^k\ensuremathβ 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 D2^\ensuremathψ\ensuremath-d, and present numerical support for these results.