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Analysis of the spectrum of a particle on a triangular lattice with two magnetic fluxes by algebraic and numerical methods. (English) Zbl 0738.35047

Summary: We consider an electron on a triangular lattice with two magnetic fluxes. Using a \(C^*\)-algebra formalism a perturbation theory around rational fluxes is developed. This semiclassical type of analysis leads to the Wilkinson-Rammal formula for the energy eigenvalues. The analytic result is verified numerically with high accuracy up to second order. Crossing of eigenvalues near band edges is shown analytically as well as numerically.

MSC:

35P05 General topics in linear spectral theory for PDEs
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