Dynamical processes in exactly solvable quantum mechanical systems

Sachiko Kitajima, Fumiaki Shibata

Sachiko Kitajima, 領子 山上, Fumiaki Shibata

Dynamics and decoherence are studied in a theoretical model in which an incident particle interacts with an array of harmonic oscillators. This system is analogous to the generalized Coleman-Hepp model treated in the previous paper and can also be formulated systematically and solved exactly. In spite of the similarities there exist certain differences between the two. We give detailed numerical calculations and discussions on the decoherence processes.

Dmitry Mozyrsky

Sachiko Kitajima, Fumiaki Shibata

Decoherence and relaxation processes in quantum systems are studied on the basis of an exactly solvable model. That is, a generalized Coleman-Hepp model is analyzed in a framework of a spin coherent state representation which enables us to determine time evolution of the whole system as successive applications of rotation operators. A density matrix of the whole system and reduced density matrices of constituent subsystems are obtained to yield quasi-probability densities and averages of observables of an incident particle and a detector (reservoir) system. Numerical evaluation of these quantities is performed to find decoherence like phenomena for larger values of N (a number of detector spins) and S l (magnitude of a detector spin). An appearance of a mixed state (i.e., vanishing of off-diagonal elements of a reduced matrix) is explicitly shown when N and/or S l become infinity. Namely, this occurs in the thermodynamic limit ( N →∞) and/or in the classical apparatus limit ( S l →∞).

Sergio A Albeverio, Friedrich Gesztesy, Raphael J. Høegh-Krohn +1 more

Sergio A Albeverio, Fritz Gesztesy, Raphael J. Høegh-Krohn +1 more