During the last few years quantum graphs have become a paradigm of quantum chaos with
applications from spectral statistics to chaotic scattering and wavefunction statistics. In the …

We give a self-contained presentation of the theory of self-adjoint extensions using the
technique of boundary triples. A description of the spectra of self-adjoint extensions in terms …

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 …

This open access book gives a systematic introduction into the spectral theory of differential
operators on metric graphs. Main focus is on the fundamental relations between the …

We consider a family of non-compact manifolds X ε (“graph-like manifolds”) approaching a
metric graph X 0 and establish convergence results of the related natural operators, namely …

Abstract The Kreĭn-Naĭmark formula provides a parametrization of all selfadjoint exit space
extensions of a (not necessarily densely defined) symmetric operator in terms of maximal …

We consider magnetic Schrödinger operators on quantum graphs with identical edges. The
spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the …

In this paper we define (local) Dirac operators and magnetic Schrödinger Hamiltonians on
fractals and prove their (essential) self-adjointness. To do so we use the concept of 1-forms …

We consider a quantum graph as a model of graphene in magnetic fields and give a
complete analysis of the spectrum, for all constant fluxes. In particular, we show that if the …

We consider a quantum graph as a model of graphene in constant magnetic field and
describe the density of states in terms of relativistic Landau levels satisfying a Bohr …