Surgery principles for the spectral analysis of quantum graphs
From MaRDI portal
Publication:5234516
DOI10.1090/tran/7864zbMath1451.34029arXiv1807.08183OpenAlexW3100247963WikidataQ128060235 ScholiaQ128060235MaRDI QIDQ5234516
Gregory Berkolaiko, Delio Mugnolo, Pavel Kurasov, James Bernard Kennedy
Publication date: 26 September 2019
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1807.08183
Estimates of eigenvalues in context of PDEs (35P15) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)
Related Items (41)
Distinguishing cospectral quantum graphs by scattering ⋮ Spectral preorder and perturbations of discrete weighted graphs ⋮ Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs ⋮ Standing waves on quantum graphs ⋮ Quantum trees which maximize higher eigenvalues are unbalanced ⋮ Doubly nonlinear Schrödinger ground states on metric graphs ⋮ A theory of spectral partitions of metric graphs ⋮ Eventual domination for linear evolution equations ⋮ Symmetry breaking in two-dimensional square grids: persistence and failure of the dimensional crossover ⋮ Impediments to diffusion in quantum graphs: Geometry-based upper bounds on the spectral gap ⋮ Ground states for the NLS equation with combined local nonlinearities on noncompact metric graphs ⋮ Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation ⋮ Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge ⋮ Surgery transformations and spectral estimates of \(\delta\) beam operators ⋮ Sturm-Liouville problems and global bounds by small control sets and applications to quantum graphs ⋮ Mean distance on metric graphs ⋮ Peaked and Low Action Solutions of NLS Equations on Graphs with Terminal Edges ⋮ A Family of Diameter-Based Eigenvalue Bounds for Quantum Graphs ⋮ Spectral Monotonicity for Schrödinger Operators on Metric Graphs ⋮ Standing waves on a flower graph ⋮ \(n\)-Laplacians on metric graphs and almost periodic functions. I ⋮ Degenerate band edges in periodic quantum graphs ⋮ On the hot spots of quantum graphs ⋮ Bi-Laplacians on graphs and networks ⋮ Multi-pulse edge-localized states on quantum graphs ⋮ Uniqueness and non-uniqueness of prescribed mass NLS ground states on metric graphs ⋮ On the eigenvalues of quantum graph Laplacians with large complex \(\delta\) couplings ⋮ The Krein-von Neumann extension for Schrödinger operators on metric graphs ⋮ Asymptotics and estimates for spectral minimal partitions of metric graphs ⋮ Reducible Fermi surface for multi-layer quantum graphs including stacked graphene ⋮ Edge-localized states on quantum graphs in the limit of large mass ⋮ Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs ⋮ On Pleijel's nodal domain theorem for quantum graphs ⋮ Laplacians on bipartite metric graphs ⋮ Lower estimates on eigenvalues of quantum graphs ⋮ Sharp diameter bound on the spectral gap for quantum graphs ⋮ Disjointness-preserving operators and isospectral Laplacians ⋮ On the Spectral Gap for Networks of Beams ⋮ On torsional rigidity and ground-state energy of compact quantum graphs ⋮ On extremal eigenvalues of the graph Laplacian * ⋮ The statistics of spectral shifts due to finite rank perturbations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the spectral gap of a quantum graph
- Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph
- Rayleigh estimates for differential operators on graphs
- The number of nodal domains on quantum graphs as a stability index of graph partitions
- NLS ground states on graphs
- Pucci eigenvalues on geodesic balls
- Negative energy ground states for the \(L^{2}\)-critical NLSE on metric graphs
- A lower bound for nodal count on discrete and metric graphs
- A conjecture on the algebraic connectivity of connected graphs with fixed girth
- Methods of intermediate problems for eigenvalues. Theory and ramifications
- Quantum graphs which optimize the spectral gap
- Spectral surgery technology for quantum graphs
- Extremal properties of eigenvalues for a metric graph.
- Genericity of simple eigenvalues for a metric graph
- Perturbation theory for linear operators.
- A characteristic equation associated to an eigenvalue problem on \(c^ 2\)-networks
- On the ground state of quantum graphs with attractive \(\delta \)-coupling
- On the hot spots of quantum graphs
- Semi-classical measures on quantum graphs and the Gauß map of the determinant manifold
- Limits of quantum graph operators with shrinking edges
- Semigroup methods for evolution equations on networks
- The algebraic connectivity of graphs with given circumference
- A theory of spectral partitions of metric graphs
- Star graphs and \v Seba billiards
- Schrödinger operators on graphs: Symmetrization and Eulerian cycles
- Ground State on the Dumbbell Graph
- Lack of Ground State for NLSE on Bridge-Type Graphs
- Eigenvalue estimates for the Laplacian on a metric tree
- Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs
- Extremizing algebraic connectivity subject to graph theoretic constraints
- Ground States for NLS on Graphs: a Subtle Interplay of Metric and Topology
- An elementary introduction to quantum graphs
- Spectral Monotonicity for Schrödinger Operators on Metric Graphs
- Spectral gap for quantum graphs and their edge connectivity
- 7 Spectral inequalities in quantitative form
- Edge connectivity and the spectral gap of combinatorial and quantum graphs
- Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths
This page was built for publication: Surgery principles for the spectral analysis of quantum graphs
