Quantum Transport Properties of Schrödinger Operator with a Quasi-Periodic Potential in Dimension Two

Math Physics Seminar
Tuesday, November 7, 2017 - 10:00am for 1 hour (actually 50 minutes)
Skiles 006
Yulia Karpeshina – University of Alabama, Birmingham – karpeshi@uab.edu
Michael Loss
Existence of ballistic transport for Schr ̈odinger operator with a quasi- periodic potential in dimension two is discussed. Considerations are based on the following properties of the operator: the spectrum of the operator contains a semiaxis of absolutely continuous spectrum and there are generalized eigenfunctions being close to plane waves ei⟨⃗k,⃗x⟩ (as |⃗k| → ∞) at every point of this semiaxis. The isoenergetic curves in the space of momenta ⃗k corresponding to these eigenfunctions have a form of slightly distorted circles with holes (Cantor type structure).