What Determines the Spreading of a Wave Packet?

Journal Article · Mon Sep 01 00:00:00 EDT 1997 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.79.1959· OSTI ID:542282

Ketzmerick, R; Geisel, T ^[1]; Ketzmerick, R; Kruse, K; Geisel, T ^[2]; Kruse, K; Kraut, S ^[3]

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1. Institute for Theoretical Physics, University of California, Santa Barbara, California 93106 (United States)
2. Max-Planck-Institut fuer Stroemungsforschung und Institut fuer Nichtlineare Dynamik der Universitaet Goettingen, Bunsenstrasse 10, D-37073 Goettingen (Germany)
3. Institut fuer Theoretische Physik und SFB Nichtlineare Dynamik, Universitaet Frankfurt, D-60054 Frankfurt/Main (Germany)

The multifractal dimensions D{sup {mu}}{sub 2} and D{sup {psi}}{sub 2} 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 k th moment increases as t{sup k{beta}} with {beta}=D{sup {mu}}{sub 2}/D{sup {psi} }{sub 2} , while, in general, t{sup 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{sup {psi}}{sub 2}{minus}d , and present numerical support for these results. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 542282
• Journal Information: Physical Review Letters, Vol. 79, Issue 11; Other Information: PBD: Sep 1997
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
WAVE PACKETS
SHAPE
ENERGY SPECTRA
EIGENFUNCTIONS
SCALING
WIDTH