  The states of an open quantum system interact ("talk") with one another via
the extended environment into which the localized system is embedded. This
interaction is mediated by the source term of the Schr\"odinger equation which
describes the coupling between system and environment. The source term is
nonlinear and causes width bifurcation and, respectively, level repulsion. It
is strong only in the neighborhood of singular (exceptional) points. We provide
typical results for the phase rigidity and the mixing of the biorthogonal
eigenfunctions of the Hamiltonian. A completely unexpected result is that the
phase rigidity approaches a value near to one (characteristic of orthogonal
eigenfunctions) when width bifurcation (or level repulsion) becomes maximum.
This behavior of the phase rigidity is caused exclusively by the nonlinearity
of the source term of the Schr\"odinger equation. The eigenfunctions remain
mixed in the set of original wavefunctions also under these critical
conditions. Eventually, a dynamical phase transition occurs. This process is
irreversible. It allows, among others, a physical interpretation of the
well-known resonance trapping phenomenon. Our results for the eigenvalues and
eigenfunctions of a non-Hermitian Hamiltonian are supported by experimental
results obtained in different systems. The relation of our results for open
quantum systems under critical conditions to those in optics and photonics with
PT-symmetry breaking is considered. As a result, the balance between gain and
loss is a very interesting general phenomenon that may occur in many different
systems.
