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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 89
Explicit Computation of the Discriminant for the Harper Equation with Rational Flux Ch. Kreft
A central role in the spectral analysis of the Harper equation with rational flux is played by its discriminant which is computed explicitely in this paper. Its coefficients are sums of trigonometric polynomials. The result applies directly to the formula for the density of states. Furthermore we compute the nullspace of the Hofstadter matrix for all rational fluxes and all Bloch vectors.
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