21 citations · 81 across the 8 of their papers we have counts for
6 papers · 1 filter
Bound States for Nano-Tubes with a Dislocation
Rainer Hempel, Martin Kohlmann, Marko Stautz +1
As a model for an interface in solid state physics, we consider two real-valued potentials and on the cylinder or tube $S=\mathbb R \times (\mathbb R/\mathbb Z)…
On Open Scattering Channels for Manifolds with Ends
Rainer Hempel, Olaf Post, Ricardo Weder
In the framework of time-dependent geometric scattering theory, we study the existence and completeness of the wave operators for perturbations of the Riemannian metric for the Lap…
Dislocation problems for periodic Schrödinger operators and mathematical aspects of small angle grain boundaries
Rainer Hempel, Martin Kohlmann
We discuss two types of defects in two-dimensional lattices, namely (1) translational dislocations and (2) defects produced by a rotation of the lattice in a half-space. For Lipsch…
Spectral Properties of Grain Boundaries at Small Angles of Rotation
Rainer Hempel, Martin Kohlmann
We study some spectral properties of a simple two-dimensional model for small angle defects in crystals and alloys. Starting from a periodic potential , we le…
A variational approach to dislocation problems for periodic Schrödinger operators
Rainer Hempel, Martin Kohlmann
As a simple model for lattice defects like grain boundaries in solid state physics we consider potentials which are obtained from a periodic potential on with p…
Spectral Gaps for Periodic Elliptic Operators with High Contrast: an Overview
Rainer Hempel, Olaf Post
We discuss the band-gap structure and the integrated density of states for periodic elliptic operators in the Hilbert space , for . We specifically consider sit…