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 …

An overview over the microwave studies of chaotic systems is presented, performed by the
authors and their co-workers in Marburg and Nice. In an historical overview the impact of …

One of the most important characteristics of a quantum graph is the average density of
resonances, ρ=(L/π), where L denotes the length of the graph. This is a very robust measure …

Quantum mechanics is quite an unintuitive theory, in which experience from our common life
often fails to describe the results of experiments. However, a mathematical theory based on …

We study the spectral gap, ie the distance between the two lowest eigenvalues for Laplace
operators on metric graphs. A universal lower estimate for the spectral gap is proven and it is …

It has been suggested that the distribution of the suitably normalized number of zeros of
Laplacian eigenfunctions contains information about the geometry of the underlying domain …

We consider the resonances of a quantum graph G that consists of a compact part with one
or more infinite leads attached to it. We discuss the leading term of the asymptotics of the …

The structure of a network has a major effect on dynamical processes on that network. Many
studies of the interplay between network structure and dynamics have focused on models of …

We investigate the high-energy eigenvalue asymptotics of quantum graphs consisting of the
vertices and edges of the five Platonic solids considering two different types of the vertex …

We study asymptotical behaviour of resonances for a quantum graph consisting of a finite
internal part and external leads placed into a magnetic field, in particular, the question …