Resonant states of open quantum systems

TL;DR

This paper demonstrates that quantum resonant states conserve particle number, provides a novel expansion of Green's functions in open quantum systems, and interprets Fano asymmetry as interference between discrete states.

Contribution

It introduces a background-integral-free resonant-state expansion for Green's functions and offers a microscopic derivation of Fano parameters in open quantum systems.

Findings

Resonant states conserve particle number.

Green's function expansion involves only discrete eigenstates.

Fano asymmetry arises from interference between eigenstates.

Abstract

We first show that quantum resonant states observe particle number conservation and hence are consistent with the probabilistic interpretation of quantum mechanics. We then present for a class of quantum open systems, a resonant-state expansion of the sum of the retarded and advanced Green's functions. The expansion is given purely in terms of all discrete eigenstates and does not contain any background integrals. Using the expansion, we argue that the Fano asymmetry of resonance peaks is interpreted as interference between discrete eigenstates. We microscopically derive the Fano parameters for several cases.