Bandwidths Statistics from the Eigenvalue Moments for Harper-Hofstadter Problem
Abstract
I propose a method for studying the product of bandwidths for the Harper-Hofstader model. This method requires knowledge of the moments of the midband energies. I conjectured a general formula for these moments. I computed the asymptotic representation for the product of bandwidths in the limit of a weak magnetic flux using Szego's theorem for Hankel matrices. I then give a first approximation for the edge of the butterfly spectrum and discuss its connection with P. Levy's formula for Brownian motion .
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