21 citations · 132 across the 37 of their papers we have counts for
9 papers · 1 filter
Coarse geometry and its applications in solid state physics
Matthias Ludewig
In this article, we give an overview over recent developments in the mathematical treatment of topological insulators using coarse geometry.
Quantization of conductance and the coarse cohomology of partitions
Matthias Ludewig, Guo Chuan Thiang
We demonstrate how integer quantization of Hall conductance arises from the large-scale geometry of the sample. Specifically, the Hall conductance is a higher-trace pairing of the…
Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory
Matthias Ludewig
In this paper, we study Lagrangian correspondences between Hilbert spaces. A main focus is the question when the composition of two Lagrangian correspondences is again Lagrangian.…
Large-scale geometry obstructs localization
Matthias Ludewig, Guo Chuan Thiang
We explain the coarse geometric origin of the fact that certain spectral subspaces of topological insulator Hamiltonians are delocalized, in the sense that they cannot admit an ort…
Delocalized spectra of Landau operators on helical surfaces
Yosuke Kubota, Matthias Ludewig, Guo Chuan Thiang
On a flat surface, the Landau operator, or quantum Hall Hamiltonian, has spectrum a discrete set of infinitely degenerate Landau levels. We consider surfaces with asymptotically co…
Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry
Matthias Ludewig, Guo Chuan Thiang
We use coarse index methods to prove that the Landau Hamiltonian on the hyperbolic half-plane, and even on much more general imperfect half-spaces, has no spectral gaps. Thus the e…
Cobordism invariance of topological edge-following states
Matthias Ludewig, Guo Chuan Thiang
We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore…
Good Wannier bases in Hilbert modules associated to topological insulators
Matthias Ludewig, Guo Chuan Thiang
For a large class of physically relevant operators on a manifold with discrete group action, we prove general results on the (non-)existence of a basis of smooth well-localised Wan…
Asymptotic eigenfunctions for Schrödinger operators on a vector bundle
Matthias Ludewig, Elke Rosenberger
In the limit , we analyze a class of Schrödinger operators acting on sections of a vector bundle ove…