An elementary introduction to quantum graphs
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Publication:4608449
DOI10.1090/conm/700/14182zbMath1388.34020arXiv1603.07356OpenAlexW4238371686MaRDI QIDQ4608449
Publication date: 16 March 2018
Published in: Geometric and Computational Spectral Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1603.07356
Sturm-Liouville theory (34B24) General spectral theory of ordinary differential operators (34L05) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)
Related Items (31)
Spectral properties of quantum circulant graphs ⋮ A matrix Schrödinger approach to focusing nonlinear Schrödinger equations with nonvanishing boundary conditions ⋮ Concrete method for recovering the Euler characteristic of quantum graphs ⋮ Spectral enclosures for non-self-adjoint extensions of symmetric operators ⋮ On the quotient quantum graph with respect to the regular representation ⋮ Nodal statistics on quantum graphs ⋮ The heat kernel on the diagonal for a compact metric graph ⋮ Impediments to diffusion in quantum graphs: Geometry-based upper bounds on the spectral gap ⋮ Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons ⋮ Absolutely continuous spectrum for Laplacians on radial metric trees and periodicity ⋮ UNIQUE SOLVABILITY OF IBVP FOR PSEUDO-SUBDIFFUSION EQUATION WITH HILFER FRACTIONAL DERIVATIVE ON A METRIC GRAPH ⋮ Localized eigenvectors on metric graphs ⋮ Time evolution and the Schrödinger equation on time dependent quantum graphs * ⋮ From the AKNS system to the matrix Schrödinger equation with vanishing potentials: Direct and inverse problems ⋮ Initial boundary value problem for a time fractional wave equation on a metric graph ⋮ Fokas method for the heat equation on metric graphs ⋮ Degenerate band edges in periodic quantum graphs ⋮ Limiting eigenfunctions of Sturm-Liouville operators subject to a spectral flow ⋮ Neumann domains on quantum graphs ⋮ NLS bifurcations on the bowtie combinatorial graph and the Dumbbell metric graph ⋮ Nodal deficiency, spectral flow, and the Dirichlet-to-Neumann map ⋮ Instability of static solutions of the sine-Gordon equation on a \(\mathcal{Y}\)-junction graph with \(\delta\)-interaction ⋮ Localization and landscape functions on quantum graphs ⋮ Spectral solutions of PDEs on networks ⋮ Soliton and breather splitting on star graphs from tricrystal Josephson junctions ⋮ Limits of quantum graph operators with shrinking edges ⋮ Surgery principles for the spectral analysis of quantum graphs ⋮ Quantum graphs via exercises ⋮ Instability theory of kink and anti-kink profiles for the sine-Gordon equation on Josephson tricrystal boundaries ⋮ Locating Conical Degeneracies in the Spectra of Parametric Self-adjoint Matrices ⋮ Unstable kink and anti-kink profile for the sine-Gordon equation on a \({\mathcal{Y}} \)-junction graph
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