Phys. Rev. Lett. 79, 1959–1963 (1997)What Determines the Spreading of a Wave Packet?Received 23 October 1996; published in the issue dated 15 September 1997 The multifractal dimensions D2μ and D2ψ 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 tkβ with β = D2μ/D2ψ, while, in general, tkβ 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 D2ψ-d, and present numerical support for these results. © 1997 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.79.1959
DOI:
10.1103/PhysRevLett.79.1959
PACS:
03.65.-w, 05.45.+b, 71.30.+h
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