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Center for Nonlinear Studies |
Hofstadter problem is about a quantum mechanics of one particle moving on a 2D lattice in a quantized magnetic field. Despite of its seeming simplicity the problem is notoriously complicated. If the flux per a lattice plaquette is an irrational number, the spectrum is known to be a singular continuum - an inhumanly complex Cantor set of gaps and bands collapsing to points. For many years this problem was a synonym of an unmanageable complexity. Some time ago together with A. Zabrodin and A. Abanov we found that the problem is Bethe Ansatz-integrable due to a delicate symmetry possessed by the problem. The Bethe-Ansatz equations uncover some features of the singular continuum spectrum, but the most interesting scaling features of the spectrum remain unknown. I review some of these works.
Host: Razvan Teodorescu