Bandwidths Statistics from the Eigenvalue Moments for Harper-Hofstadter Problem
arXiv:cond-mat/9910225 · doi:10.1088/0305-4470/33/39/305
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 .
LaTeX, 18 pages, 2 figures