Resonance scattering and singularities of the scattering function

W. D. Heiss; R. G. Nazmitdinov

doi:10.1140/epjd/e2010-00088-5

EPJ

Resonance scattering and singularities of the scattering function

W. D. Heiss¹ and R. G. Nazmitdinov²^,3

¹ National Institute for Theoretical Physics, Stellenbosch Institute for Advanced Study, and Institute of Theoretical Physics, University of Stellenbosch, 7602 Matieland, South Africa
² Department de Física, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain
³ Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia

Received: 20 January 2010
Revised: 8 March 2010
Published online: 6 April 2010

Abstract

Recent studies of transport phenomena with complex potentials are explained by generic square root singularities of spectrum and eigenfunctions of non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that such singularities produce a significant effect upon the pole behaviour of the scattering matrix, and more significantly upon the associated residues. This mechanism explains why by proper choice of the system parameters the resonance cross section is increased drastically in one channel and suppressed in the other channel.