Dynamical semigroups for interacting quantum and classical systems

Authors
Citation
R. Olkiewicz, Dynamical semigroups for interacting quantum and classical systems, J MATH PHYS, 40(3), 1999, pp. 1300-1316
Citations number
21
Categorie Soggetti
Physics
Journal title
JOURNAL OF MATHEMATICAL PHYSICS
ISSN journal
00222488 → ACNP
Volume
40
Issue
3
Year of publication
1999
Pages
1300 - 1316
Database
ISI
SICI code
0022-2488(199903)40:3<1300:DSFIQA>2.0.ZU;2-D
Abstract
A mathematical framework for the completely positive semigroup coupling bet ween classical and quantum systems is proposed. The coupling ensures a flow of information from the quantum system to the classical one and the influe nce of the classics on the dynamics of the quantum system in a dissipative way. The classical evolution on average is modified by the expectation valu e of some quantum operator. Examples of a classical particle moving along a geodesic line in a curved space interacting with the quantum system, and t he coupling of a two state quantum system to all pure states, are discussed . (C) 1999 American Institute of Physics. [S0022-2488(99)00803-8].