Spectral Properties of Schrödinger Operators on Perturbed Lattices
arXiv:1408.2076 · doi:10.1007/s00023-015-0430-0
Abstract
We study the spectral properties of Schrödinger operators on perturbed lattices. We shall prove the non-existence or the discreteness of embedded eigenvalues, the limiting absorption principle for the resolvent, construct a spectral representation, and define the S-matrix. Our theory covers the square, triangular, diamond, Kagome lattices, as well as the ladder, the graphite and the subdivision of square lattice.
References in corpus (1)
Cited by in corpus (20)
- Spectral Properties of Schrödinger Operators on Perturbed Lattices
- Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues
- Generalized eigenfunctions and scattering matrices for position-dependent quantum walks
- Scattering on periodic metric graphs
- Irreducibility of the Bloch Variety for Finite-Range Schrödinger Operators
- Spectral and scattering theory for Schrödinger operators on perturbed topological crystals
- Inverse scattering for Schrödinger operators on perturbed lattices
- Detection of edge defects by embedded eigenvalues of quantum walks
- Continuum limit for lattice Schrödinger operators
- Spectral and scattering theory for Gauss-Bonnet operators on perturbed topological crystals
- Spectral and scattering theory for topological crystals perturbed by infinitely many new edges
- Long-range scattering theory for discrete Schrödinger operators on graphene
- Fermi isospectrality for discrete periodic Schrodinger operators
- Asymptotic properties of generalized eigenfunctions for multi-dimensional quantum walks
- Scattering the geometry of weighted graphs
- Continuum limit for Laplace and Elliptic operators on lattices
- Inverse scattering on the quantum graph -- Edge model for graphen
- Inverse scattering on the quantum graph for graphene
- Clusters of resonances for a non-selfadjoint multichannel discrete Schrödinger operator
- Eigenvalues of periodic difference operators on lattice octant