Remarks on the relation between quantum dynamics and fractal spectra

被引：32
作者：
Barbaroux, JM [1 ]
Combes, JM [1 ]
Montcho, R [1 ]
机构：
[1] UNIV TOULON & VAR,DEPT MATH,F-83957 LA GARDE,FRANCE
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1997年 / 213卷 / 02期
关键词：
D O I：
10.1006/jmaa.1997.5571
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate the large time behaviour of various solutions of the Schrodinger equation in terms of some local and global dimensions of the spectral measure. We emphasize in particular the role of the Hausdorff and correlation dimensions for the growth exponents of position moments. We also discuss the stability of such exponents under local perturbations. (C) 1997 Academic Press.
引用
收藏
页码：698 / 722
页数：25
相关论文
共 23 条
  • [1] [Anonymous], DIFFERENTIAL EQUATIO
  • [2] SPECTRAL PROPERTIES OF ONE DIMENSIONAL QUASI-CRYSTALS
    BELLISSARD, J
    IOCHUM, B
    SCOPPOLA, E
    TESTARD, D
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1989, 125 (03) : 527 - 543
  • [3] BELLISSARD J, 1995, J PHYS CONDENS MATT, V7, P3507
  • [4] SPECTRAL PROPERTIES OF ONE-DIMENSIONAL SCHRODINGER-OPERATORS WITH POTENTIALS GENERATED BY SUBSTITUTIONS
    BOVIER, A
    GHEZ, JM
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1993, 158 (01) : 45 - 66
  • [5] Operators with singular continuous spectrum .4. Hausdorff dimensions, rank one perturbations, and localization
    delRio, R
    Jitomirskaya, S
    Last, Y
    Simon, B
    [J]. JOURNAL D ANALYSE MATHEMATIQUE, 1996, 69 : 153 - 200
  • [6] FALCONER KJ, 1985, CAMBRIDGE TRACTS MAT
  • [7] SPECTRAL PROPERTIES OF QUANTUM DIFFUSION ON DISCRETE LATTICES
    GUARNERI, I
    [J]. EUROPHYSICS LETTERS, 1989, 10 (02): : 95 - 100
  • [8] GUARNERI I, 1994, ANN I H POINCARE-PHY, V61, P369
  • [9] GUARNERI I, 1995, WORKSH SING SPECTR I
  • [10] Scattering on fractal measures
    Guerin, CA
    Holschneider, M
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1996, 29 (23): : 7651 - 7667
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