Resonant-state expansion of the Green's function of open quantum systems

TL;DR

This paper reviews recent work on the transmission coefficient in open quantum systems, showing it can be expressed as a sum over discrete eigenstates, revealing insights into resonance behaviors and Fano asymmetry.

Contribution

It introduces a new expression for the transmission coefficient as a sum over discrete eigenstates, clarifying the origin of resonance peaks and asymmetries in open quantum systems.

Findings

Transmission coefficient expressed as a sum over eigenstates

Fano asymmetry caused by interference between eigenstates

Unstable resonances can skew nearby resonance peaks

Abstract

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent "background" is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.