Quantum graphs and their applications : proceedings of an AMSIMSSIAM Joint Summer Research Conference on Quantum Graphs and Their Applications, June 1923, 2005, Snowbird, Utah

Contributor(s): Berkolaiko GregoryMaterial type: Computer fileComputer fileSeries: Contemporary mathematics ; v. 415Publication details: Providence, R.I. : American Mathematical Society, c2006Description: 1 online resource (ix, 307 p. : ill.)ISBN: 9780821880944 (online)Subject(s): Quantum graphsOnline resources: Click here to access online
Contents:
Fluctuationbased proof of the stability of ac spectra of random operators on tree graphs ; Metrized graphs, Laplacian operators, and electrical networks ; Form factor expansion for large graphs: a diagrammatic approach ; The spectral form factor for quantum graphs with spinorbit coupling ; Linear network models related to blood flow ; Localization on AvronExnerLast graphs. I. Local perturbations ; Weighted Laplacians and the sigma function of a graph ; Approximations of permutationsymmetric vertex couplings in quantum graphs ; Resistance of random Sierpinski gaskets ; Small diffusion asymptotics for exit problems on graphs ; Determinant of the Schrodinger operator on a metric graph ; Local spectral density and vacuum energy near a quantum graph vertex ; What are zeta functions of graphs and what are they good for? ; Fluctuation statistics for quantum star graphs ; Laplacians on metric graphs: eigenvalues, resolvents and semigroups ; Transition from a network of thin fibers to the quantum graph: an explicitly solvable model ; On the limiting absorption principle and spectra of quantum graphs ; Quantum mechanics, superconductivity and fluid flow in narrow networks ; A relation between the bond scattering matrix and the spectral counting function for quantum graphs ; The quantum graph as a limit of a network of physical wires ; On the trace formula for quantum star graphs Michael Aizenman Robert Sims and Simone Warzel ; Matthew Baker and Xander Faber ; Gregory Berkolaiko ; Jens Bolte and Jonathan Harrison ; Robert Carlson ; Kingwood Chen Stanislav Molchanov and Boris Vainberg ; Fan Chung and Ross M Richardson ; Pavel Exner and Ondrej Turek ; Daniel Fontaine Thomas Smith and Alexander Teplyaev ; Mark Freidlin and Matthias Weber ; Leonid Friedlander ; Stephen A Fulling ; Matthew D Horton H M Stark and Audrey A Terras ; J P Keating ; Vadim Kostrykin and Robert Schrader ; Stanislav Molchanov and Boris Vainberg ; BengSeong Ong ; Jacob Rubinstein ; Holger Schanz ; Uzy Smilansky and Michael Solomyak ; B Winn
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Includes bibliographical references.

Fluctuationbased proof of the stability of ac spectra of random operators on tree graphs ; Metrized graphs, Laplacian operators, and electrical networks ; Form factor expansion for large graphs: a diagrammatic approach ; The spectral form factor for quantum graphs with spinorbit coupling ; Linear network models related to blood flow ; Localization on AvronExnerLast graphs. I. Local perturbations ; Weighted Laplacians and the sigma function of a graph ; Approximations of permutationsymmetric vertex couplings in quantum graphs ; Resistance of random Sierpinski gaskets ; Small diffusion asymptotics for exit problems on graphs ; Determinant of the Schrodinger operator on a metric graph ; Local spectral density and vacuum energy near a quantum graph vertex ; What are zeta functions of graphs and what are they good for? ; Fluctuation statistics for quantum star graphs ; Laplacians on metric graphs: eigenvalues, resolvents and semigroups ; Transition from a network of thin fibers to the quantum graph: an explicitly solvable model ; On the limiting absorption principle and spectra of quantum graphs ; Quantum mechanics, superconductivity and fluid flow in narrow networks ; A relation between the bond scattering matrix and the spectral counting function for quantum graphs ; The quantum graph as a limit of a network of physical wires ; On the trace formula for quantum star graphs Michael Aizenman Robert Sims and Simone Warzel ; Matthew Baker and Xander Faber ; Gregory Berkolaiko ; Jens Bolte and Jonathan Harrison ; Robert Carlson ; Kingwood Chen Stanislav Molchanov and Boris Vainberg ; Fan Chung and Ross M Richardson ; Pavel Exner and Ondrej Turek ; Daniel Fontaine Thomas Smith and Alexander Teplyaev ; Mark Freidlin and Matthias Weber ; Leonid Friedlander ; Stephen A Fulling ; Matthew D Horton H M Stark and Audrey A Terras ; J P Keating ; Vadim Kostrykin and Robert Schrader ; Stanislav Molchanov and Boris Vainberg ; BengSeong Ong ; Jacob Rubinstein ; Holger Schanz ; Uzy Smilansky and Michael Solomyak ; B Winn

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