Bandwidths Statistics from the Eigenvalue Moments for Harper-Hofstadter Problem
Mesoscale and Nanoscale Physics
2009-10-31 v1 Strongly Correlated Electrons
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 .
Keywords
Cite
@article{arxiv.cond-mat/9910225,
title = {Bandwidths Statistics from the Eigenvalue Moments for Harper-Hofstadter Problem},
author = {O. Lipan},
journal= {arXiv preprint arXiv:cond-mat/9910225},
year = {2009}
}
Comments
LaTeX, 18 pages, 2 figures