Classical limit. Dissipation and quantum measurement

A. PLASTINO; A.M. KOWALSKI

Understanding Time Evolution

Nova Science Publishers

Lugar: New York; Año: 2020; p. 1 - 24

The interplay between quantum and classical systems, is a subject of current interest. Consider two coupled systems. If quantum effects in one of them are small with regards to the other, that one regards as classical greatly simplifies the description and yields deep insight into the composite system´s dynamics. In this methodology, we consider that the evolution of quantum operators is canonical, with the total Hamiltonian and that the generator of the temporal evolution of the classical variables, is the mean value of this Hamiltonian, evaluated with a purely quantum Density Matrix. As a result, all the properties of the quantum system are fulfilled at any time, even when considering dissipation. This methodology can not only represent a good approximation, but it can be the one that describes the interaction between microscopic and macroscopic systems, as in the case of the interaction of a quantum system with a bath or in that of a measurement process.