A sum rule for the dispersion relations of the rational Harper equation
- 21 November 1992
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 25 (22) , 6123-6133
- https://doi.org/10.1088/0305-4470/25/22/033
Abstract
The authors derive an exact sum rule satisfied by the dispersion relations of the commensurable case of Harper's equation (1955). They use this result to derive a lower bound for the total bandwidth of the spectrum and to provide a stronger analytical justification for a result due to Thouless (1990) concerning the total bandwidth when the commensurability is a high order rational.Keywords
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