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- W1947584178 abstract "A discrete WKB approximation is applied to Harper's equation describing the motion of an electron in a square lattice subject to a magnetic field. The treatment is valid when the modulation parameter (proportional to the magnetic field) is a rational number M/N, in the limit of large N. A uniform asymptotic expression is derived for the Floquet wavenumber which characterizes the dynamics and spectral properties. The case of energies near the classical separatrix, crucial to the properties of the spectrum near the transition between localized and extended states is included. An application is a detailed calculation of the total width of the bands in the critical region, for M=1 and 2. The results are consistent with Thouless' conjecture that the bandwidth obeys a universal scaling form, independent of M." @default.
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