Quasiperiodic Operators with Monotone Potentials: Sharp Arithmetic Spectral Transitions and Small Coupling Localization

Friday, October 31, 2014 - 9:30am - 10:30am
Keller 3-180
Svetlana Jitomirskaya (University of California)
It is well known that spectral properties of quasiperiodic
operators depend rather delicately on the arithmetics of the parameters
involved. Consequently, obtaining results for all parameters often
requires considerably more difficult arguments than for a.e. parameter,
and does offer a deeper insight. In the first part of the talk we will report
the first result of this kind in regard to the spectral decomposition:
full description of spectral types of the Maryland model for all (in
contrast with a.e., known for ~30 years) values of frequency, phase, and coupling (with nontrivial dependence on the arithmetics). In the second part of the talk
we show that for (a large class of) bounded monotone potentials there is
Anderson localization for all non-zero couplings.