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Spectral dimension and dynamics for Harper's equation

Physical Review B, ISSN: 0163-1829, Vol: 50, Issue: 3, Page: 1420-1429
1994
  • 61
    Citations
  • 0
    Usage
  • 4
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    61
    • Citation Indexes
      61
  • Captures
    4

Article Description

The spectrum of Harper's equation (a model for Bloch electrons in a magnetic field) is a fractal Cantor set if the ratio β of the area of a unit cell to that of a flux quantum is not a rational number. It has been conjectured that the second moment of an initially localized wave packet has a power-law growth of the form x2∼t02D, where D0 is the box-counting dimension of the spectrum, and that D0=1/2. We present numerical results on the dimension of the spectrum and the spread of a wave packet indicating that these relationships are at best approximate. We also present heuristic arguments suggesting that there should be no general relationships between the dimension and the spread of a wave packet. © 1994 The American Physical Society.

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