Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs

DOI10.1063/1.4937119zbMath1335.81078arXiv1503.07245OpenAlexW3099640657MaRDI QIDQ3463252

Ram Band, Gregory Berkolaiko, Tracy Weyand

Publication date: 12 January 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.07245

zbMATH Keywords

dispersion relationquantum graphnodal count

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Operations with distributions and generalized functions (46F10) Electromagnetic theory (general) (78A25) Dispersion theory, dispersion relations arising in quantum theory (81U30) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (12)

Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph ⋮ Quantum graphs which optimize the spectral gap ⋮ Eigenvalue estimates for the Laplacian on a metric tree ⋮ Morse theory for discrete magnetic operators and nodal count distribution for graphs ⋮ An elementary introduction to quantum graphs ⋮ Edge connectivity and the spectral gap of combinatorial and quantum graphs ⋮ Neumann domains on quantum graphs ⋮ Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs ⋮ Laplacians on bipartite metric graphs ⋮ On the nodal structure of nonlinear stationary waves on star graphs ⋮ Surgery principles for the spectral analysis of quantum graphs ⋮ A local test for global extrema in the dispersion relation of a periodic graph

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Recovering quantum graphs from their Bloch spectrum
• Nodal count of graph eigenfunctions via magnetic perturbation
• Magnetic interpretation of the nodal defect on graphs
• Dynamics of nodal points and the nodal count on a family of quantum graphs
• The number of nodal domains on quantum graphs as a stability index of graph partitions
• Spectral analysis on graph-like spaces
• Essential self-adjointness for combinatorial Schrödinger operators. III: Magnetic fields
• On the spectra of carbon nano-structures
• A lower bound for nodal count on discrete and metric graphs
• Some inequalities between Dirichlet and Neumann eigenvalues
• Periodic orbit theory and spectral statistics for quantum graphs
• Fluxes, Laplacians, and Kasteleyn's theorem
• Oscillation properties of the spectrum of a boundary value problem on a graph
• Quantum wires with magnetic fluxes
• Symmetry and Dirac points in graphene spectrum
• Genericity of simple eigenvalues for a metric graph
• Wave packets in honeycomb structures and two-dimensional Dirac equations
• Laplacian eigenvectors of graphs. Perron-Frobenius and Faber-Krahn type theorems
• Quantum graph spectra of a graphyne structure
• The nodal count {0,1,2,3,…} implies the graph is a tree
• Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions
• On the location of spectral edges in \mathbb {Z}-periodic media
• Nodal domains on graphs - How to count them and why?
• Quantum graphs: an introduction and a brief survey
• Eigenvalue and nodal properties on quantum graph trees*
• On occurrence of spectral edges for periodic operators inside the Brillouin zone
• Eigenvectors of acyclic matrices
• On an inequality between Dirichlet and Neumann eigenvalues for the Laplace operator
• Honeycomb lattice potentials and Dirac points
• Graph models for waves in thin structures
• Nodal counting on quantum graphs
• Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths
• Forces in Molecules
• Floquet theory for partial differential equations
• Differential operators on graphs and photonic crystals

This page was built for publication: Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs