Time Relativity in the Dynamics of Open Quantum Systems

Abstract

When describing the dynamics of quantum systems interacting with a coherent external electromagnetic field, the instant at which the exciting (measuring) field begins to act is traditionally taken as zero time in the laboratory frame. Using the concept of coherence sudden death in an observed quantum system, we introduce the definition of local, completely incoherent subensembles of the quantum system in which it is found with a certain probability at each instant of time in the process of a continuous observation (measurement). For such subensembles an arbitrary instant of time in the laboratory frame is the initial time of the interaction with the external (measuring) field. As a result, the dynamics of an open quantum system is represented by a superposition of the dynamics of local subsystems with a continuous distribution of the times at which the interaction with the external field begins. We have derived an expression for the dynamical “multitime” contribution to the stationary solution of the Bloch equations, which clearly demonstrates the meaning of time relativity in the dynamics of two-level quantum systems in the semiclassical approximation. This dynamical multitime contribution is shown to explain the emergence of quantum beats at zero frequency (the Hanle effect, the level crossing) in EPR.