Spectral dimension and dynamics for Harper's equation
Physical Review B, ISSN: 0163-1829, Vol: 50, Issue: 3, Page: 1420-1429
1994
- 61Citations
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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.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=7044232264&origin=inward; http://dx.doi.org/10.1103/physrevb.50.1420; http://www.ncbi.nlm.nih.gov/pubmed/9976327; https://link.aps.org/doi/10.1103/PhysRevB.50.1420; http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevB.50.1420/fulltext; http://link.aps.org/article/10.1103/PhysRevB.50.1420
American Physical Society (APS)
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