Abstract
The scaling of the total width of the band for the discrete Mathieu equation is studied in the critical region near the transition between localized and extended states, for the special case in which there is one period of the modulation forp lattice spacings. A general expression for the bandwidthW in the critical region is found. At the critical point an analytic expression forpW is found which agrees to one part in 108 with the result deduced from numerical work.
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Communicated by B. Simon
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Thouless, D.J. Scaling for the discrete Mathieu equation. Commun.Math. Phys. 127, 187–193 (1990). https://doi.org/10.1007/BF02096501
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DOI: https://doi.org/10.1007/BF02096501