Special Session 185: Multiscale Analysis: Geometry and Evolution Problems (mSPACE)

On the asymptotic behavior of the spectral gap for discrete Schr\{o}dinger operators
Matthias Hofmann
FernUniversit\"at in Hagen
Germany
Co-Author(s):    Joachim Kerner, Maximilian Pechmann
Abstract:
We investigates the asymptotic behavior of the spectral gap of a class of discrete Schr\{o}dinger operators defined on a path graph in the limit of infinite volume. We confirmed recent results and generalized them to a larger class of potentials using entirely different methods. Notably, we also resolved a conjecture previously proposed in this context, which yields new insights into the rate at which the spectral gap tends to zero as the volume increases. This is joint work with Joachim Kernen (FernUniversit\{a}t in Hagen) and Maximilian Pechmann (Tennesse Technology University).