No quantum ergodicity for star graphs

DOI10.1007/s00220-004-1145-0zbMath1059.81066arXivmath-ph/0308005OpenAlexW3100584744MaRDI QIDQ1766908

Xianqiang Yang

Publication date: 2 March 2005

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

Full work available at URL: https://arxiv.org/abs/math-ph/0308005

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quantum chaos (81Q50)

Related Items

Quantum ergodicity on regular graphs ⋮ Quantum ergodicity for point scatterers on arithmetic tori ⋮ Quantum ergodicity for quantum graphs without back-scattering ⋮ Scattering resonances of large weakly open quantum graphs ⋮ Spectral properties of quantum circulant graphs ⋮ Quantum ergodicity for graphs related to interval maps ⋮ Eigenfunction statistics on quantum graphs ⋮ The heat kernel on the diagonal for a compact metric graph ⋮ Superscars for arithmetic point scatters II ⋮ Quantum ergodicity for large equilateral quantum graphs ⋮ The ergodicity landscape of quantum theories ⋮ Visibility of quantum graph spectrum from the vertices ⋮ Maximal scarring for eigenfunctions of quantum graphs ⋮ Superscars for arithmetic toral point scatterers ⋮ Semi-classical measures on quantum graphs and the Gauß map of the determinant manifold ⋮ Relationship between scattering matrix and spectrum of quantum graphs ⋮ Quantum ergodicity for expanding quantum graphs in the regime of spectral delocalization ⋮ Pseudo-differential calculus on homogeneous trees ⋮ Multifractal eigenfunctions for a singular quantum billiard ⋮ Localized eigenfunctions in Šeba billiards ⋮ Quantum ergodicity on large regular graphs ⋮ Spectrum of a non-selfadjoint quantum star graph ⋮ Rényi and Tsallis entropies related to eigenfunctions of quantum graphs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ergodicity and eigenfunctions of the Laplacian
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• Smoothed wave functions of chaotic quantum systems
• Linear and nonlinear theory of eigenfunction scars
• Periodic orbit theory and spectral statistics for quantum graphs
• Ergodic properties of eigenfunctions for the Dirichlet problem
• Value distribution of the eigenfunctions and spectral determinants of quantum star graphs
• Scarred eigenstates for quantum cat maps of minimal periods
• Families of line-graphs and their quantization
• Equipartition of the eigenfunctions of quantized ergodic maps on the torus
• Star graphs and \v Seba billiards
• The cat maps: quantum mechanics and classical motion
• Regular and irregular semiclassical wavefunctions
• Quantum graphs: a simple model for chaotic scattering
• Form factor for a family of quantum graphs: an expansion to third order
• Spectral statistics for the Dirac operator on graphs
• Occupation times distribution for Brownian motion on graphs
• The local time distribution of a particle diffusing on a graph
• The spin contribution to the form factor of quantum graphs
• Wave chaos in singular quantum billiard
• Unitary-stochastic matrix ensembles and spectral statistics
• Scattering theory on graphs
• Orbit bifurcations and the scarring of wave functions
• Two-point spectral correlations for star graphs
• Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
• Form factor for large quantum graphs: evaluating orbits with time reversal
• Nodal counting on quantum graphs
• On the level spacing distribution in quantum graphs.