Quantum graphs: an introduction and a brief survey
arXiv:0802.3442 · doi:10.1016/j.compstruc.2012.03.001
Abstract
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary, i.e. they refer to other surveys.
References in corpus (12)
- Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder
- Vacuum Energy and Repulsive Casimir Forces in Quantum Star Graphs
- Repulsive Casimir Pistons
- Convergence of resonances on thin branched quantum wave guides
- Large gaps in point-coupled periodic systems of manifolds
- Approximations of singular vertex couplings in quantum graphs
- Localization on a quantum graph with a random potential on the edges
- Quantum Field Theory on Star Graphs
- Zigzag periodic nanotube in magnetic field
- Nodal domains on graphs - How to count them and why?
- Point interactions in acoustics: one dimensional models
- Quantum graphs with spin Hamiltonians
Cited by in corpus (31)
- The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
- Junctions of anyonic Luttinger wires
- Dirichlet forms and semilinear elliptic equations with measure data
- Parabolic systems with coupled boundary conditions
- Energy flow and fluctuations in non-equilibrium conformal field theory on star graphs
- Properties of Black Hole Radiation From Tunnelling
- Isospectral graphs with identical nodal counts
- Zeta functions of quantum graphs
- Non-Weyl resonance asymptotics for quantum graphs in a magnetic field
- Direct computation of scattering matrices for general quantum graphs
- Shape Optimization Problems for Metric Graphs
- The nonlinear Schrödinger equation: A mathematical model with its wide-ranging applications
- Non-equilibrium current cumulants and moments with a point-like defect
- Edge switching transformations of quantum graphs
- Quantum graphs -- Generic eigenfunctions and their nodal count and Neumann count statistics
- Inverse problems in geometric graphs using internal measurements
- Quantum Fluctuations of Entropy Production for Fermionic Systems in Landauer-Buttiker State
- Path Integral Junctions
- Modeling active optical networks
- A Gelfand-Levitan trace formula for generic quantum graphs
- Trace formulae for Schrodinger operators on metric graphs with applications to recovering matching conditions
- Existence of guided waves due to a lineic perturbation of a 3D periodic medium
- A Frucht's theorem for quantum graphs
- Trace formulae for graph Laplacians with applications to recovering matching conditions
- Discovering hidden layers in quantum graphs
- Eigenvalue bracketing for discrete and metric graphs
- Boundary systems and (skew-)self-adjoint operators on infinite metric graphs
- Hardy uniqueness principle for the linear Schrodinger equation on quantum regular trees
- Semiclassical Length Measure from a Quantum-Gravity Wave Function
- Finite deficiency indices and uniform remainder in Weyl's law
- Pseudodifferential operators on periodic graphs