Semi-classical measures on quantum graphs and the Gauß map of the determinant manifold
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Publication:2256014
DOI10.1007/s00023-014-0326-4zbMath1306.81043arXiv1311.5449OpenAlexW2963621517MaRDI QIDQ2256014
Publication date: 19 February 2015
Published in: Annales Henri Poincaré (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1311.5449
Elliptic equations on manifolds, general theory (58J05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)
Related Items (26)
Quantum ergodicity on regular graphs ⋮ Quantum ergodicity for quantum graphs without back-scattering ⋮ Scattering resonances of large weakly open quantum graphs ⋮ Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph ⋮ Nodal statistics on quantum graphs ⋮ Quantum graphs which optimize the spectral gap ⋮ The heat kernel on the diagonal for a compact metric graph ⋮ Spectral determinants and an Ambarzumian type theorem on graphs ⋮ Quantum ergodicity for large equilateral quantum graphs ⋮ Exotic eigenvalues of shrinking metric graphs ⋮ An Ambarzumian-type theorem on graphs with odd cycles ⋮ An elementary introduction to quantum graphs ⋮ Visibility of quantum graph spectrum from the vertices ⋮ Maximal scarring for eigenfunctions of quantum graphs ⋮ A Family of Diameter-Based Eigenvalue Bounds for Quantum Graphs ⋮ Non-compact quantum graphs with summable matrix potentials ⋮ Stable polynomials and crystalline measures ⋮ Neumann domains on quantum graphs ⋮ Topological resonances on quantum graphs ⋮ Quantum ergodicity for expanding quantum graphs in the regime of spectral delocalization ⋮ On fully supported eigenfunctions of quantum graphs ⋮ Surgery principles for the spectral analysis of quantum graphs ⋮ On torsional rigidity and ground-state energy of compact quantum graphs ⋮ Spectrum of a dilated honeycomb network ⋮ Spectrum of a non-selfadjoint quantum star graph ⋮ Rényi and Tsallis entropies related to eigenfunctions of quantum graphs
Cites Work
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- Eigenfunction statistics on quantum graphs
- Ergodicity and eigenfunctions of the Laplacian
- Uniform distribution of eigenfunctions on compact hyperbolic surfaces
- The spectrum of the continuous Laplacian on a graph
- Value distribution of the eigenfunctions and spectral determinants of quantum star graphs
- No quantum ergodicity for star graphs
- Genericity of simple eigenvalues for a metric graph
- The nodal count {0,1,2,3,…} implies the graph is a tree
- Relationship between scattering matrix and spectrum of quantum graphs
- On the level spacing distribution in quantum graphs.
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