Quasibound states at thresholds in multichannel impurity scattering

TL;DR

This paper studies the behavior of quasibound states at thresholds in multichannel impurity scattering, revealing their persistence and influence on physical quantities despite previous claims of their disappearance.

Contribution

It clarifies the threshold behavior of quasibound states in multichannel scattering and challenges prior assumptions about their disappearance at subband boundaries.

Findings

Quasibound states persist at thresholds and influence physical observables.

Transmission line shape and Friedel sum rule indicate survival of quasibound states.

Provides a general discussion on boundary conditions in multichannel scattering.

Abstract

We investigate the threshold behavior 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 behavior of transmission resonances, and quasibound states and their boundary conditions in the general context of multichannel scatterings.