Isolated zeros in the spectral function as signature of a quantum continuum

TL;DR

This paper demonstrates that in quantum systems with at least two isolated states coupled to a continuum, the spectral function of one state shows an isolated zero at the energy of the other, providing a potential tool for detecting quantum continua.

Contribution

It generalizes the understanding of spectral functions in quantum systems, revealing a universal zero feature that can indicate the presence of a continuum spectrum.

Findings

Spectral functions exhibit isolated zeros at specific energies.

The phenomenon is applicable to various quantum systems with continua.

Potential use as an indirect detection method for quantum continua.

Abstract

We study the observable properties of quantum systems which involve a quantum continuum as a subpart. We show in a very general way that in any system, which consists of at least two isolated states coupled to a continuum, the spectral function of one of the states exhibits an isolated zero at the energy of the other state. Several examples of quantum systems exhibiting such isolated zeros are discussed. Although very general, this phenomenon can be particularly useful as an indirect detection tool for the continuum spectrum in the lab realizations of quantum critical behavior.