Scattering from a Ring Graph - A Simple Model for the Study of Resonances

D. Waltnera and U. Smilanskya, b aDepartment of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel bSchool of Mathematics, Cardiff University, Cardiff, Wales, UK

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Scattering from the very simple ring graph is shown to display several basic features which underlie the complex (chaotic) phenomena observed in scattering from more complex graphs. In particular we demonstrate the appearance of arbitrarily narrow resonances - the "topological resonances" which are directly linked to the existence of cycles. We use the ring graph to study the response of such resonances to perturbations induced by a time-dependent random noise.

DOI: 10.12693/APhysPolA.124.1087 PACS numbers: 05.40.Ca, 05.45.Mt, 03.65.Sq, 02.10.Ox