The number of nodal domains on quantum graphs as a stability index of graph partitions

DOI10.1007/s00220-011-1384-9zbMath1244.81026arXiv1103.1423OpenAlexW2016979060MaRDI QIDQ422394

Uzy Smilansky, Ram Band, Hillel Raz, Gregory Berkolaiko

Publication date: 16 May 2012

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

Full work available at URL: https://arxiv.org/abs/1103.1423

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (26)

Isospectral discrete and quantum graphs with the same flip counts and nodal counts ⋮ Concrete method for recovering the Euler characteristic of quantum graphs ⋮ Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs ⋮ Courant-sharp eigenvalues of Neumann 2-rep-tiles ⋮ Regularity of all minimizers of a class of spectral partition problems ⋮ A theory of spectral partitions of metric graphs ⋮ 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 a magnetic characterization of spectral minimal partitions ⋮ Stability of spectral partitions and the Dirichlet-to-Neumann map ⋮ Minimizing optimal transport for functions with fixed-size nodal sets ⋮ Rayleigh estimates for differential operators on graphs ⋮ Critical partitions and nodal deficiency of billiard eigenfunctions ⋮ Spectral minimal partitions of unbounded metric graphs ⋮ On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes ⋮ A Family of Diameter-Based Eigenvalue Bounds for Quantum Graphs ⋮ Neumann domains on quantum graphs ⋮ On the hot spots of quantum graphs ⋮ On the ground state for quantum graphs ⋮ Asymptotics and estimates for spectral minimal partitions of metric graphs ⋮ Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs ⋮ On Pleijel's nodal domain theorem for quantum graphs ⋮ On the nodal structure of nonlinear stationary waves on star graphs ⋮ Surgery principles for the spectral analysis of quantum graphs ⋮ On Molchanov's condition for the spectrum discreteness of a quantum graph Hamiltonian with \(\delta\)-coupling ⋮ Extremality conditions and regularity of solutions to optimal partition problems involving Laplacian eigenvalues

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