Maximal scarring for eigenfunctions of quantum graphs

DOI10.1088/1361-6544/aad3fezbMath1397.81079arXiv1803.08311OpenAlexW3101340189MaRDI QIDQ5374508

No author found.

Publication date: 14 September 2018

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.08311

zbMATH Keywords

entropyquantum graphsscarring

Mathematics Subject Classification ID

Quantum chaos (81Q50) (S)-matrix theory, etc. in quantum theory (81U20) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Measures of information, entropy (94A17) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantum ergodicity for quantum graphs without back-scattering
• Eigenfunction statistics on quantum graphs
• Entropy of semiclassical measures for nonpositively curved surfaces
• Entropy of semiclassical measures of the Walsh-quantized Baker's map
• Ergodic billiards that are not quantum unique ergodic (with an appendix by Andrew Hassell and Luc Hillairet)
• Graph eigenfunctions and quantum unique ergodicity
• Smoothed wave functions of chaotic quantum systems
• Pseudo-laplaciens. I
• Periodic orbit theory and spectral statistics for quantum graphs
• Scarred eigenstates for quantum cat maps of minimal periods
• On the maximal scarring for quantum cat map eigenstates
• No quantum ergodicity for star graphs
• Semi-classical measures on quantum graphs and the Gauß map of the determinant manifold
• Entropy and the localization of eigenfunctions
• Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms
• Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold
• Invariant measures and arithmetic unique ergodicity. Appendix by E. Lindenstrauss and D. Rudolph
• Star graphs and \v Seba billiards
• The cat maps: quantum mechanics and classical motion
• Spectral statistics of a pseudo-integrable map: the general case
• Is computing with the finite Fourier transform pure or applied mathematics?
• Inverse eigenvalue problems on directed graphs
• Scars in quantum chaotic wavefunctions
• Form factor for a family of quantum graphs: an expansion to third order
• Spectral statistics for the Dirac operator on graphs
• Semiclassical criterion for scars in wave functions of chaotic systems
• Unitary-stochastic matrix ensembles and spectral statistics
• Orbit bifurcations and the scarring of wave functions
• Two-point spectral correlations for star graphs
• Rényi and Tsallis entropies related to eigenfunctions of quantum graphs
• Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
• Quantum graphs where back-scattering is prohibited
• Form factor for large quantum graphs: evaluating orbits with time reversal
• Quantum graphs: I. Some basic structures
• On the level spacing distribution in quantum graphs.

This page was built for publication: Maximal scarring for eigenfunctions of quantum graphs