Quantum Institute: Visitor Schedule

The Quantum Lunch is regularly held on Thursdays in the Theoretical Division Conference Room, TA-3, Building 123, Room 121.
For more information, contact Diego Dalvit.
To add your name to the Quantum Lunch email list, contact Charlotte Carter

Thursday, June 4, 2009
12:30 PM - 2:00 PM

Speaker: Paul Wiegmann, University of Chicago

Technical Host:

TOPIC: Integrable complexity: Hofstadter Problem

Abstract
The Hofstadter problem is about quantum mechanics of one particle moving on a 2D lattice in a quantized magnetic field. Despite its seeming simplicity, the problem is notoriously complicated. If the flux per 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 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 system. 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.