Topics on Fermi varieties of discrete periodic Schrödinger operators

Abstract

This is a survey of recent progress on the irreducibility of Fermi varieties, rigidity results and embedded eigenvalue problems of discrete periodic Schrödinger operators.

arXiv commentSpecial Collection on the Proceedings of ICMP XX

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• Criteria for embedded eigenvalues for discrete Schrödinger operators
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• Generic properties of dispersion relations for discrete periodic operators
• Reducible Fermi surface for multi-layer quantum graphs including stacked graphene
• Topics on Fermi varieties of discrete periodic Schrödinger operators
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• Discrete Bethe-Sommerfeld Conjecture
• Zeroes of the spectral density of the periodic Schroedinger operator with Wigner-von Neumann potential
• Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian
• Periodic and limit-periodic discrete Schrödinger operators
• Irreducibility of the Fermi Surface for Planar Periodic Graph Operators
• Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach
• Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von Neumann approach
• Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique
• Fermi isospectrality for discrete periodic Schrodinger operators
• Examples of fourth-order scattering-type operators with embedded eigenvalues in their continuous spectra

Cited by in corpus (4)

• Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues
• Irreducibility of the Bloch Variety for Finite-Range Schrödinger Operators
• Topics on Fermi varieties of discrete periodic Schrödinger operators
• Fermi isospectrality of discrete periodic Schrödinger operators with separable potentials on ${\mathbb{Z}}^2$