Branch points in the complex plane and information loss in quantum systems at high level density

The mechanism of avoided level crossings in quantum systems is studied. It is traced back to the existence of branch points in the complex plane which influence the properties of resonance states as well as of discrete states. An avoided level crossing of two states causes not only an exchange of the two wave functions but, above all, correlations between them. The correlations play an important role at high level density since they cause the loss of information on the individual properties of the states.