Dynamical semigroups for interacting quantum and classical systems

Abstract

A mathematical framework for the completely positive semigroup coupling between classical and quantum systems is proposed. The coupling ensures a flow of information from the quantum system to the classical one and the influence of the classics on the dynamics of the quantum system in a dissipative way. The classical evolution on average is modified by the expectation value of some quantum operator. Examples of a classical particle moving along a geodesic line in a curved space interacting with the quantum system, and the coupling of a two state quantum system to all pure states, are discussed.