Semiquantum Time Evolution II: Density Matrices

A.M. KOWALSKI; A. PLASTINO

Understanding Time Evolution

Nova Science Publishers

Lugar: New York; Año: 2020; p. 25 - 53

In this chapter, we introduce the general MaxEnt Density Matrix for systems where quantum and classical degrees of freedom interact. Consider two coupled systems. One is quantum for sure. If quantum effects in the other one are small with regards to those of the first system, the second can be regarded as classical, which greatly simplifies the description. This methodology can not only represent a good approximation, but it can be the one that describes the interaction between microscopic and macroscopic degrees of freedom. We consider that the evolution of quantum operators is the canonical one and that the generator of the temporal evolution of the classical variables is the mean value of the total Hamiltonian. As a result, all the properties of the quantum system are fulfilled at any time. In particular, the Density Matrix always verifies the Liouville´s equation, describing situations where the Principle of Uncertainty coexists with Chaos and Dissipation.