Dynamical stabilization and time in open quantum systems

The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is non-Hermitian. Its imaginary part is the time operator. As a rule, time and energy vary continuously when controlled by a parameter. At high level density, where many states avoid crossing, a dynamical phase transition takes place in the system under the influence of the environment. It causes a dynamical stabilization of the system what can be seen in many different experimental data. Due to this effect, time is bounded from below: the decay widths (inverse proportional to the lifetimes of the states) do not increase limitless. The dynamical stabilization is an irreversible process.