Scaling, localization and bandwidths for equations with competing periods

D.J. Thouless and Yong Tan

Physica A: Statistical Mechanics and its Applications, 1991, vol. 177, issue 1, 567-577

Abstract: The finite size scaling theory of the measure of the spectrum of Harper's equation is reexamined. For sequences of fractions tending to a rational limit a simple criterion is derived which determines whether the corrections to scaling behave as (log p)−2 or p−2 as the denominator p is increased. The question of how special are the properties of the Harper equation, is studied. It is shown that if the pure cosine term in the diagonal term is replaced by a distorted periodic function the different subbands undergo a transition from “localized” to “extended” at a value of the strength of the off-diagonal term that depends on energy, in contrast to the Harper equation where the transition is energy-independent. This has a crucial effect on the measure of the spectrum.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:177:y:1991:i:1:p:567-577

DOI: 10.1016/0378-4371(91)90202-N

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