Zero measure Cantor spectrum for Schrödinger operators with quasi-periodic potentials
A talk in the Keine Reihe series by
Philipp Gohlke
| Abstract: | Spectral properties of Schrödinger operators determine the time evolution of an associated quantummechanical system. Zero measure Cantor spectrum - first considered to be a rather exotic exception- is shown to be "generic" (in an appropriate sense) for more and more classes of potentialfunctions.The phenomen is well-known for so-called Sturmian sequences which arise from minimimaltranslations on the one-dimensional torus. More generally, quasi-periodic potentials are obtained bysampling along translation orbits on a finite-dimensional torus. Built on recent developments thatrelate torus translations to multidimensional continued fraction algorithms and generalizedsubstitution systems, we show that zero measure Cantor spectrum can be found for almost everytwo-dimensional torus translations.This is joint work with Jonathan Chaika, David Damanik and Jake Fillman.
This talk takes place within the retreat of the CRC 1283. All members of the CRC are invited to attend. Please contact ckoehler@math.uni-bielefeld.de for Zoom-Link, Meeting-ID and Password. |