Measure of the spectra of periodic graph operators in the large-coupling limit

2025/11/02 by Jake Fillman, Fillman, Jake · 1 citation
Mathematics · #35J10 #Advanced Operator Algebra Research #FOS: Mathematics #Graph theory and applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2511.00757

openalex publication_date 2025/11/02 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

Abstract

We derive a sharp criterion on the spectra of periodic discrete Schrödinger operators acting on connected periodic lattices: the measure of the spectrum goes to zero as the coupling constant goes to infinity if and only if there is no infinite connected path of degeneracies.

Citations

• Sharp Polynomial Velocity Decay Bounds for Multidimensional Periodic Schrödinger Operators
• Absence of flat bands for discrete periodic graph operators with generic potentials
• Optimal dispersion for discrete periodic Schrödinger operators
• Dispersive Decay Estimates for periodic Jacobi operators on the half-line
• Slow propagation velocities in Schrödinger operators with large periodic potential
• Algebraic Properties of the Fermi Variety for Periodic Graph Operators
• Flat bands of periodic graphs
• Ballistic transport in periodic and random media
• Two-sided estimates of total bandwidth for Schrödinger operators on periodic graphs
• Discrete Bethe--Sommerfeld Conjecture for Triangular, Square, and Hexagonal Lattices
• Invariants for Laplacians on periodic graphs
• Reducible Fermi Surfaces for Non-symmetric Bilayer Quantum-Graph Operators
• Spectra of Discrete Two-Dimensional Periodic Schrödinger Operators with Small Potentials
• An overview of periodic elliptic operators
• Schrödinger operators on periodic discrete graphs

Cited by

• On measure estimates arising from Hausdorff distance convergence

Related

• Asymptotics and estimates of the discrete spectrum of the Schrodinger operator on a discrete periodic graph
• Schrödinger operators on periodic discrete graphs
• Asymptotic isospectrality of Schrödinger operators on periodic graphs
• Schrödinger operators with guided potentials on periodic graphs
• On continuous spectrum of magnetic Schrödinger operators on periodic discrete graphs