  We consider the behaviour of open quantum systems in dependence on the
coupling to one decay channel by introducing the coupling parameter $\alpha$
being proportional to the average degree of overlapping. Under critical
conditions, a reorganization of the spectrum takes place which creates a
bifurcation of the time scales with respect to the lifetimes of the resonance
states. We derive analytically the conditions under which the reorganization
process can be understood as a second-order phase transition and illustrate our
results by numerical investigations. The conditions are fulfilled e.g. for a
picket fence with equal coupling of the states to the continuum. Energy
dependencies within the system are included. We consider also the generic case
of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the
reorganization of the spectrum occurs at the critical value $\alpha_{crit}$ of
the control parameter globally over the whole energy range of the spectrum. All
states act cooperatively.
