DYNAMICS OF THE INTERACTION BETWEEN CLASSICAL AND QUANTUM SYSTEMS AND THE REDUCTION OF THE WAVE PACKET

Dariusz Chruściński, Andrzej Kossakowski

Rolando Rebolledo

Ph. Blanchard, Arkadiusz Jadczyk

Zbigniew Haba

We discuss a quantum-mechanical analog of the classical angle variable. A localized wave packet is constructed generalizing the conventional coherent state of minimal uncertainty. For small ħ the wave packet moves along a certain trajectory close to the classical torus. In a class of integrable Hamiltonian systems we estimate that the wave packet preserves its shape at least for times of order [Formula: see text].

J. R. Anglin, SALMAN HABIB

The dynamics of linear quantum systems is classical in the Wigner representation, yet linear problems are often analyzed using such general techniques as influence functionals and Bogoliubov transformations. In fact, the classical equations of motion provide a simpler and more intuitive formalism for these systems. As an important example, we show that quantum Brownian dynamics in the independent oscillator model is described directly and completely by a c-number Langevin equation. The corresponding Fokker-Planck equation is always local in time, regardless of the environmental spectrum.

Fabio Bagarello