Phase transitions in open quantum systems

We consider the behavior of open quantum systems through the dependence of the coupling to one decay channel by introducing the coupling parameter alp ha, which is proportional to the average degree of overlapping. Under criti cal conditions, a reorganization of the spectrum takes place that creates a bifurcation of the time scales with respect to the lifetimes of the resona nce states. We derive analytically the conditions under which the reorganiz ation process can be understood as a second-order phase transition and illu strate our results by numerical investigations. The conditions are fulfille d, e.g., for a uniform picket-fence level distribution with equal coupling of the states to the continuum. Energy dependencies within the system are i ncluded. We consider also the case of an unfolded Gaussian orthogonal ensem ble and of a spectrum bounded from below. In all these cases, the reorganiz ation of the spectrum occurs at the critical value alpha(crit) of the contr ol parameter globally over the whole energy range of the spectrum. All stat es act cooperatively. [S1.063-651X(99)02707-5].