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 …

A brief survey on graph models for wave propagation in thin structures is presented. Such
models arise in many areas of mathematics, physics, chemistry and engineering (dynamical …

We formulate and discuss one-particle quantum scattering theory on an arbitrary finite graph
with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator …

This monograph explains the theory of quantum waveguides, that is, dynamics of quantum
particles confined to regions in the form of tubes, layers, networks, etc. The focus is on …

A quantum graph is a graph equipped with a self-adjoint differential or pseudodifferential
Hamiltonian. Such graphs have been studied recently in relation to some problems of …

We quantize graphs (networks) which consist of a finite number of bonds and vertices. We
show that the spectral statistics of fully connected graphs is well reproduced by random …

In order to become worldly things, that is, deeds and facts and events and patterns of
thoughts or ideas,[action, speech, and thought] must first be seen, heard, and remembered …

The paper deals with some spectral properties of (mostly infinite) quantum and
combinatorial graphs. Quantum graphs have been intensively studied lately due to their …

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 …

Recent developments in the quantum mechanical description of open systems are
presented. In particular, the specific properties of the deep quantum region are pointed out …