Large time behavior of lossy systems governed by Dirac and Schrödinger operators.

We discuss the behaviour at large times of systems with losses. Typical examples involve Schrödinger or Dirac evolution governed by complex potentials and the linear transport operator. When the losses are weak the evolution resembles the situation in the selfadjoint scattering theory. At the opposite end, when the losses get strong the evolution reduces to the exponential decay. In the talk we are going to discuss an intermediate regime where the losses are strong enough to prevent scattering but too weak to move the spectrum off the real line and cause the exponential decay.