An analytical approach to atomic multichannel collisions in tight harmonic waveguides

摘要

We perform an analytical investigation in the framework of generalized $K$matrix theory of the scattering problem in tight isotropic and harmonicwaveguides allowing for several open scattering channels. The scatteringbehavior is explored for identical bosons and fermions, as well as fordistinguishable particles, the main aspect being the confinement-inducedresonances (CIR) which are attributed to different partial waves. In particularwe present the unitarity bounds which emerge when considering a quasi onedimensional system. Unitarity bounds are also given for the transitioncoefficients, which show the limitations for efficient transversal(de-)excitations by means of CIRs. We analyze the CIR for $d$-waves and findthe intriguing phenomenon of a strong transmission suppression in the presenceof more than one open channel, which represents an interesting regime to beapplied in the corresponding many-particle systems. The corresponding channelthreshold singularities are studied and it is shown that these are solelydetermined by the symmetry class of the partial wave.