Eur. Phys. J. D (2014) 68: 284
https://doi.org/10.1140/epjd/e2014-50379-8

Regular Article

Fano-Feshbach resonances in two-channel scattering around exceptional points

¹ Department of Physics, University of Stellenbosch, 7602 Matieland, South Africa
² National Institute for Theoretical Physics (NITheP), Western Cape, South Africa
³ Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70 569 Stuttgart, Germany

^a e-mail: dieter@physics.sun.ac.za

Received: 13 May 2014
Received in final form: 11 June 2014
Published online: 2 October 2014

Abstract

It is well-known that in open quantum systems resonances can coalesce at an exceptional point, where both the energies and the wave functions coincide. In contrast to the usual behaviour of the scattering amplitude at one resonance, the coalescence of two resonances invokes a pole of second order in the Green’s function, in addition to the usual first order pole. We show that the interference due to the two pole terms of different order gives rise to patterns in the scattering cross section which closely resemble Fano-Feshbach resonances. We demonstrate this by extending previous work on the analogy of Fano-Feshbach resonances to classical resonances in a system of two driven coupled damped harmonic oscillators.