Resonance Lineshapes in Quasi-One-Dimensional Scattering

TL;DR

This paper develops an S matrix approach to describe asymmetric Fano resonance lineshapes in quasi-one-dimensional scattering systems, revealing a scaling property of the asymmetry parameter q that can be tested experimentally.

Contribution

It introduces a new theoretical framework for analyzing resonance lineshapes in systems lacking continuous symmetry, highlighting the independence of the asymmetry parameter q from coupling strength.

Findings

Resonance lineshape is generally asymmetric Fano type.

The asymmetry parameter q is independent of coupling to the quasi-bound state.

The scaling property of the resonance can be experimentally tested.

Abstract

An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in microstructures or transmission resonances in waveguide junctions. The generic resonance is shown to have the asymmetric Fano lineshape. The asymmetry parameter q is independent of coupling to the quasi-bound level implying a scaling property of the resonances which can be tested in transport experiments.