Finite pseudo orbit expansions for spectral quantities of quantum graphs

DOI10.1088/1751-8113/45/32/325204zbMath1252.81066arXiv1205.4214OpenAlexW2002638014MaRDI QIDQ2907012

Ram Band, Jon M. Harrison, Christopher H. Joyner

Publication date: 5 September 2012

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

Full work available at URL: https://arxiv.org/abs/1205.4214

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (8)

Eigenvalue asymptotics for the damped wave equation on metric graphs ⋮ Spectral properties of quantum circulant graphs ⋮ An elementary introduction to quantum graphs ⋮ Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics ⋮ Lyndon word decompositions and pseudo orbits on \(q\)-nary graphs ⋮ New approach to periodic orbit theory of spectral correlations ⋮ Trace formulas for general Hermitian matrices: unitary scattering approach and periodic orbits on an associated graph ⋮ Complete dynamical evaluation of the characteristic polynomial of binary quantum graphs

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