Variational Principle for Mixed Classical-Quantum Systems
摘要
An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical variables are expressed in the form of a quantum state vector which includes the action of the classical subsystem in its phase factor. It is shown that the statistical ensemble of Brownian state vectors for a quantum particle in a classical thermal environment can be described by a density matrix evolving according to a nonlinear quantum Fokker-Planck equation. Exact solutions of this equation are obtained for a two-level system in the limit of high temperatures, considering both stationary and nonstationary initial states. A treatment of the common time shared by the quantum system and its classical environment, as a collective variable rather than as a parameter, is presented in the Appendix.
引用
@article{arxiv.quant-ph/0610011,
title = {Variational Principle for Mixed Classical-Quantum Systems},
author = {M. Grigorescu},
journal= {arXiv preprint arXiv:quant-ph/0610011},
year = {2009}
}
备注
16 pages, LaTex; added Figure 2 and Figure 3