Speaker: Dr. Rupert L. Frank (California Institute of Technology)
Date: Wednesday, June 16, 2021
Time: 1:00 PM-2:00 PM (EDT)
Zoom link: https://tennessee.zoom.us/j/97135748410
Title: On the spectrum of the Kronig–Penney model in a constant electric field
Abstract: We are interested in the nature of the spectrum of the one-dimensional Schrödinger operator whose potential is a combination of the linear Stark potential and an equidistant arrangement of delta functions. When all the coupling constants of the delta functions are equal and the strength of the electric field satisfies a rationality condition, we show that the spectrum is purely absolutely continuous away from an explicit discrete set of points. On the other hand, when the coupling constants are iid random variables, we prove that there is a transition between purely singularly continuous spectrum and purely pure point spectrum at a transition point that we compute explicitly. These models have been discussed in the solid state physics literature and our results in the first model confirms predictions by Buslaev.
The talk is based on joint work with S. Larson.