Quantum graphs: a simple model for chaotic scattering

DOI10.1088/0305-4470/36/12/337zbMath1038.81031arXivnlin/0207049OpenAlexW1992052222MaRDI QIDQ4443913

Uzy Smilansky, Tsampikos Kottos

Publication date: 19 January 2004

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0207049

zbMATH Keywords

random matricesquantum graphschaotic scattering

Mathematics Subject Classification ID

Quantum chaos (81Q50) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) (S)-matrix theory, etc. in quantum theory (81U20) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20)

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The necessity of conditions for graph quantum ergodicity and Cartesian products with an infinite graph ⋮ Scattering resonances of large weakly open quantum graphs ⋮ Relativistic quantum chaos ⋮ Association of scattering matrices in quantum networks ⋮ Imaging geometric graphs using internal measurements ⋮ Rayleigh estimates for differential operators on graphs ⋮ Dynamics of nodal points and the nodal count on a family of quantum graphs ⋮ Delay-time distribution in the scattering of time-narrow wave packets (II)—quantum graphs ⋮ On the distribution of energy of localized solutions of the Schrödinger equation that propagate along symmetric quantum graphs ⋮ Predicting the statistics of wave transport through chaotic cavities by the random coupling model: a review and recent progress ⋮ On the distribution of energy of localized solutions of the Schrödinger equation that propagate along symmetric quantum graphs ⋮ Topological resonances on quantum graphs ⋮ Approximations by graphs and emergence of global structures ⋮ No quantum ergodicity for star graphs ⋮ Edge switching transformations of quantum graphs—a scattering approach ⋮ Discrete Graphs – A Paradigm Model for Quantum Chaos ⋮ Knots and signal transmission in topological quantum devices

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