From Pure Schroedingerian to Statistical Dynamics
  Many processes in nature seem to be entirely controlled by transition rates and the corresponding statistical dynamics. Some of them are in essence quantum, like the decay of excited states, the tunneling through barriers or the decay of unstable nuclei. Thus, starting from first principles, those systems should be analyzed on the basis of the Schroedinger equation. In the present paper we consider a two level system coupled to an environment which is basically described by an two-band energy scheme. For appropriately tuned environment parameters, the excitation probability of the two level system exhibits statistical dynamics, while the full system follows the coherent, unitary pure state evolution generated by the Schroedinger equation. 
Jochen Gemmer, Mathias Michel