Non-Hamiltonian commutators in quantum mechanics.
Non-Hamiltonian commutators in quantum mechanics.
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量子力学中的非哈密尔顿换向器。
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
A. Sergi
中科院分区：
文献类型：
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作者：
A. Sergi
首先揭示了量子交换子的辛结构，然后利用它来描述量子力学中的广义非哈密顿括号。很容易认识到，量子经典系统是由这样一个括号的特定实现来描述的。在前人工作的基础上，本文解释了经典非哈密顿动力学和量子经典非哈密顿动力学的统一方法。为了说明非哈密顿交换子的用法，我们展示了如何定义量子经典系统中的热力学约束。特别地，导出了量子经典的Nosé-Hoover运动方程和相应的定态密度矩阵。给出了Nosé-Hoover链和Nosé-Andersen(恒压、恒温)动力学的非哈密顿交换子。对形式主义的观点进行了讨论。
The symplectic structure of quantum commutators is first unveiled and then exploited to describe 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 paper explains 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 Nosé-Hoover equations of motion and the associated stationary density matrix are derived. The non-Hamiltonian commutators for both Nosé-Hoover chains and Nosé-Andersen (constant-pressure, constant-temperature) dynamics are also given. Perspectives of the formalism are discussed.