Description of open quantum systems in non-Hermitian quantum mechanics

Physical examples of open quantum systems include an atom in the bath of photons or phonons, the (hypothetical) quantum computer in noisy background or any macro- or even mesoscopical system consisting of large number of the microscopical constituents whose behavior we can not explicitly describe. We discuss general issues that arise when studying models of such kind - such as decoherence, dissipation and finding the proper set of physical observables. After a brief introduction into the non-Hermitian quantum mechanics we consider a simple model demonstrating how certain kind of interaction can control the above-mentioned properties. In particular, it is explicitly shown how the interaction determines the irreducible set of observables. We also show that the same quantum system, depending on range of its parameters, may exist in two different regimes: quasi-Hermitian and strongly non-Hermitian.