Instantons and Hofstadter's Butterfly
The problem of a charged particle moving in two dimensions in the presence of a peroidic potential and a constant magnetic field was made famous by Douglas Hostadter's study of the fractal structure of the energy spectrum. This spectrum has recently been confirmed experimentally. See this Wiki page for references. Denise Freed and I were interested in studying such systems using path integral methods as a toy model of non-perturbative effects in the presence of Chern-Simons terms. These methods give some new insights into the fractal nature of the spectrum.
Research Papers
Instantons and the spectrum of Block electrons in a magnetic field, with D. Freed,
pdf
Contact Information
Email: j-harvey at uchicago.edu
Phone: +1 773-702-9897
Work Address: Enrico Fermi Institute, 5620 Ellis Ave., Chicago IL 60637 USA
