First order approach and index theorems for discrete and metric graphs

DOI10.1007/s00023-009-0001-3zbMath1206.81044arXiv0708.3707OpenAlexW2962826435MaRDI QIDQ623475

Olaf Post

Publication date: 14 February 2011

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.3707

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) (Semi-) Fredholm operators; index theories (47A53) Supersymmetry and quantum mechanics (81Q60) Index theory for dynamical systems, Morse-Conley indices (37B30) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (14)

A note on the Gaffney Laplacian on infinite metric graphs ⋮ Recovering quantum graphs from their Bloch spectrum ⋮ Generalised norm resolvent convergence: comparison of different concepts ⋮ Dirac gauge theory for topological spinors in 3+1 dimensional networks ⋮ The mass of simple and higher-order networks ⋮ The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions ⋮ Dirac and magnetic Schrödinger operators on fractals ⋮ Differential one-forms on Dirichlet spaces and Bakry-Émery estimates on metric graphs ⋮ Eigenvalue bracketing for discrete and metric graphs ⋮ Dirac-Krein systems on star graphs ⋮ Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures ⋮ Eigenvalue estimates for the Laplacian with anti-Kirchhoff conditions on a metric tree ⋮ On the viscous Burgers equation on metric graphs and fractals ⋮ Zero modes of quantum graph Laplacians and an index theorem

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