Non-Hamiltonian Commutators in Quantum Mechanics
摘要
The symplectic structure of quantum commutators is first unveiled and then exploited to introduce generalized non-Hamiltonian brackets in quantum mechanics. It is easily recognized that quantum-classical systems are described by a particular realization of such a bracket. In light of previous work, this introduces a unified approach to classical and quantum-classical non-Hamiltonian dynamics. In order to illustrate the use of non-Hamiltonian commutators, it is shown how to define thermodynamic constraints in quantum-classical systems. In particular, quantum-classical Nos\'e-Hoover equations of motion and the associated stationary density matrix are derived. The non-Hamiltonian commutators for both Nos\'e-Hoover chains and Nos\'e-Andersen (constant-pressure constant temperature) dynamics are also given. Perspectives of the formalism are discussed.
引用
@article{arxiv.quant-ph/0511076,
title = {Non-Hamiltonian Commutators in Quantum Mechanics},
author = {Alessandro Sergi},
journal= {arXiv preprint arXiv:quant-ph/0511076},
year = {2009}
}
备注
Submitted to Phys. Rev. E on August 8 2005