Schroedinger operators with pseudo-random potentials

4 June 2008, 12 noon

 

Speaker: Professor Gunter Stolz (Birmingham Alabama)

Within the theory of Schrodinger operators with ergodic potentials, two classes of potentials have been extensively studied: Random potentials (e.g. the Anderson model), and quasi-periodic potentials (e.g. the Almost Mathieu operator). Viewed as dynamical systems, these two classes represent opposite extremes within the range of ergodic potentials. We ask if other types of ergodic models allow to observe a transition between these extremes in terms of spectral phenomena. Physicists have used the term pseudo-random potentials in this context, while mathematicians seem to know embarassingly little about them. We will present some models, some results and some of the open problems.