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

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.