Scaling laws of reflection coefficients of quantum waves at a Cantor-like potential

被引：8
作者：
Sakaguchi, Hidetsugu [1 ]
Ogawana, Taichi [1 ]
机构：
[1] Kyushu Univ, Interdisciplinary Grad Sch Engn Sci, Dept Appl Sci Elect & Mat, Kasuga, Fukuoka 8168580, Japan
来源：
PHYSICAL REVIEW E | 2017年 / 95卷 / 03期
关键词：
FRACTAL MEASURES; LOCALIZATION; SETS;
D O I：
10.1103/PhysRevE.95.032214
中图分类号：
O35 [流体力学]; O53 [等离子体物理学];
学科分类号：
070204 ; 080103 ; 080704 ;
摘要：
We reconsider a one-dimensional scattering problem in the Schrodinger equation with a Cantor-like potential. The reflection coefficient obeys a scaling law for sufficiently large wave number k. The scaling law is expressed with a universal function characterized by a multifractal.
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页数：5
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共 18 条
  • [1] ALEXANDER S, 1982, J PHYS LETT-PARIS, V43, pL625, DOI 10.1051/jphyslet:019820043017062500
  • [2] Chuprikov N.L., 2008, J. Phys. A: Math. Gen, V33, P4293, DOI DOI 10.1088/0305-4470/33/23/307
  • [3] SOLUTIONS TO THE SCHRODINGER-EQUATION ON SOME FRACTAL LATTICES
    DOMANY, E
    ALEXANDER, S
    BENSIMON, D
    KADANOFF, LP
    [J]. PHYSICAL REVIEW B, 1983, 28 (06): : 3110 - 3123
  • [4] Wave propagation through Cantor-set media: Chaos, scaling, and fractal structures
    Esaki, Kenta
    Sato, Masatoshi
    Kohmoto, Mahito
    [J]. PHYSICAL REVIEW E, 2009, 79 (05):
  • [5] Scattering on fractal measures
    Guerin, CA
    Holschneider, M
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1996, 29 (23): : 7651 - 7667
  • [6] FRACTAL MEASURES AND THEIR SINGULARITIES - THE CHARACTERIZATION OF STRANGE SETS
    HALSEY, TC
    JENSEN, MH
    KADANOFF, LP
    PROCACCIA, I
    SHRAIMAN, BI
    [J]. PHYSICAL REVIEW A, 1986, 33 (02): : 1141 - 1151
  • [7] Strong resonance of light in a Cantor set
    Hatano, N
    [J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2005, 74 (11) : 3093 - 3111
  • [8] THE INFINITE NUMBER OF GENERALIZED DIMENSIONS OF FRACTALS AND STRANGE ATTRACTORS
    HENTSCHEL, HGE
    PROCACCIA, I
    [J]. PHYSICA D, 1983, 8 (03): : 435 - 444
  • [9] Rigorous solution for electromagnetic waves propagating through pre-Cantor sets
    Honda, K
    Otobe, Y
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (20): : L315 - L322
  • [10] WAVE INTERACTION WITH A FRACTAL LAYER
    KONOTOP, VV
    FEI, Z
    VAZQUEZ, L
    [J]. PHYSICAL REVIEW E, 1993, 48 (05): : 4044 - 4048
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