|
| related topics |
| {time, decoherence, evolution} |
| {energy, gaussian, time} |
| {temperature, thermal, energy} |
| {classical, space, random} |
| {field, particle, equation} |
| {equation, function, exp} |
| {group, space, representation} |
| {cos, sin, state} |
| {level, atom, field} |
| {time, wave, function} |
| {measurement, state, measurements} |
|
Variational Principle for Mixed Classical-Quantum Systems
M. Grigorescu
abstract: 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0610011
- categories:
- quant-ph cond-mat.stat-mech gr-qc
- comments:
- 16 pages, LaTex; added Figure 2 and Figure 3
- doi:
- 10.1139/P07-107
- arxiv_id:
- quant-ph/0610011
- journal_ref:
- Can. J. Phys. 85 (2007) 1023-1034
- created:
- 2006-10-02
- updated:
- 2007-06-28
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