Universal Constraint for Relaxation Rates for Quantum Dynamical Semigroup.

A general property of relaxation rates in open quantum systems is discussed. We find an interesting constraint for relaxation rates that universally holds in fairly large classes of quantum dynamics, e.g.

Feshbach projection formalism for open quantum systems.

We provide a new approach to open quantum systems which is based on the Feshbach projection method. Instead of looking for a master equation for the dynamical map acting in the space of density operators we provide the corresponding equation for the evolution in the Hilbert space of the amplitude operators. Its solution enables one to construct a legitimate quantum evolution (completely positive and trace preserving).

Non-Markovian quantum dynamics: local versus nonlocal.

We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing the evolution of such a system may be described either by a nonlocal master equation with a memory kernel or equivalently by an equation which is local in time. These two descriptions are complementary: if one is simple, the other is quite involved, or even singular, and vice versa.