Quasibound states at thresholds in multichannel impurity scattering

Abstract

We investigate the threshold behaviour of transmission resonances and quasibound states in the multichannel scattering problems of a one-dimensional (1D) time-dependent impurity potential, and the related problem of a single impurity in a quasi-1D wire. It was claimed before in the literature that a quasibound state disappears when a transmission zero collides with the subband boundary. However, the transmission line shape, the Friedel sum rule, and the delay time show that the quasibound states still survive and affect the physical quantities. We discuss the relation between threshold behaviour of transmission resonances, and quasibound states and their boundary conditions in the general context of multichannel scatterings.