acta physica slovaca

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acta physica slovaca is an internationally recognised physics journal originally established in 1950. Since 1998 listed in Current Contents. Since 2006, acta physica slovaca publishes review and tutorial articles. Papers written by specialists in a given field are intended to be accessible also to non-specialists and PhD students. Although the printed version of the journal is available, all issues are free to download from the journal's web page. We hope that the new issues of acta physica slovaca will be useful and interesting for readers.

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Current Issue


Acta Physica Slovaca 66, No.4, 265 – 363 (2016) (99 pages)

QUANTUM GRAPHS AND THEIR RESONANCE PROPERTIES

J. Lipovský
   Department of Physics, Faculty of Science, University of Hradec Králové, Rokitanského 62, 500 03 Hradec Králové, Czechia

Full text: ::pdf :: (Received 31 December 2016, accepted 23 February 2017)

Abstract: In the current review, we study the model of quantum graphs. We focus mainly on the resonance properties of quantum graphs. We define resolvent and scattering resonances and show their equivalence. We present various results on the asymptotics of the number of resolvent resonances in both non-magnetic and magnetic quantum graphs and find bounds on the coefficient by the leading term of the asymptotics. We explain methods how to find the spectral and resonance condition. Most of the notions and theorems are illustrated in examples. We show how to find resonances numerically and, in a simple example, we find trajectories of resonances in the complex plane. We discuss Fermi’s golden rule for quantum graphs and distribution of the mean intensity for the topological resonances.

PACS: 03.65.Ge, 03.65.Nk, 02.10.Ox
Keywords: Quantum graphs, Resonances, Weyl asymptotics, Scattering theory, Fermi’s golden rule
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