Special Mathematical Physics Seminar

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. 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.) 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.