Periodic and limit-periodic discrete Schrödinger operators
arXiv:1108.1584
Abstract
The theory of discrete periodic and limit-periodic Schrödinger operators is developed. In particular, the Floquet--Bloch decomposition is discussed. Furthermore, it is shown that an arbitrarily small potential can add a gap for even periods. In dimension two, it is shown that for coprime periods small potential terms don't add gaps thus proving a Bethe--Sommerfeld type statement. Furthermore limit-periodic potentials whose spectrum is an interval are constructed.
References in corpus (5)
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Cited by in corpus (6)
- Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues
- Topics on Fermi varieties of discrete periodic Schrödinger operators
- Multidimensional Almost-Periodic Schrödinger Operators with Cantor Spectrum
- Schrödinger Operators with Thin Spectra
- Expansion of the almost sure spectrum in the weak disorder regime
- On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications