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 …

Resonance and decay phenomena are ubiquitous in the quantum world. To understand
them in their complexity it is useful to study solvable models in a wide sense, that is, systems …

We discuss resonances in quantum graphs and their more general analogs having 'edges'
of different dimensions. Since the notion of resonance may mean different things, we show …

We study the model of quantum graphs with preferred-orientation coupling and state the
main results in this area. Quantum graphs describe the behaviour of a quantum particle on a …

We study a set of scattering matrices of quantum graphs containing minimal number of
passbands, ie, maximal number of zero elements. The cases of even and odd vertex degree …

V této práci se zabýváme kvantovými systémy kombinujícími dimenze jedna a tři. Konkrétně
se zabýváme systémem složeným z polopřímky a poloprostoru a systémem složeným z …

Quantum graphs are quite a simple model which studies behaviour of a quantum particle on
a network. First attempts to place a quantum particle to a graph date back to 1930's (Pauling …

This is an extended version of the talk given at the Nato Advanced Research Workshop:
New Challenges in Complex System Physics, May 20–24, 2013 in Samarkand (Uzbekistan) …