Induced vs. Spontaneous breakdown of S-matrix unitarity: Probability of no return in quantum chaotic and disordered systems

We investigate systematically sample-to-sample fluctuations of the probability τ of no return into a given entrance channel for wave scattering from disordered systems. For zero-dimensional (“quantum chaotic”) and quasi-one-dimensional systems with broken time-reversal invariance, we derive explicit formulas for the distribution of τ and investigate particular cases. Finally, relating τ to violation of S -matrix unitarity induced by internal dissipation, we use the same quantity to identify the Anderson delocalization transition as the phenomenon of spontaneous breakdown of S -matrix unitarity.