摘要翻译:
在非平衡统计算符方法(NESOM)下,利用量子经典系综导出了扩展系统中原子位置和动量随时间演化的动力学方程。离子被经典地处理,而它们的电子被量子力学地处理;然而,统计算子没有以任何方式分解,也没有关于电子子系统的简化假设。利用这种方法,我们导出了经典自由度(原子)的运动方程,它充分考虑了与量子变量(电子)的相互作用和能量交换。我们的方程,除了通常与Ehrenfest动力学相关联的类牛顿项之外,还包含了与原子速度成正比的附加项,这些附加项可以与电子摩擦力相关联。讨论了通过复杂的非平衡相关函数计算摩擦力的可能方法。特别地,我们证明了关联函数与热力学松原格林函数直接相关,并且这种关系允许在计算关联函数时用图解方法微扰地处理电子-电子相互作用。这一工作也推广了以前的尝试,主要是基于模型系统,将电子摩擦引入原子的分子动力学方程。
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英文标题:
《Non-equilibrium statistical mechanics of classical nuclei interacting
with the quantum electron gas》
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作者:
Yu Wang and Lev Kantorovich
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最新提交年份:
2007
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分类信息:
一级分类:Physics 物理学
二级分类:Statistical Mechanics 统计力学
分类描述:Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变,热力学,场论,非平衡现象,重整化群和标度,可积模型,湍流
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英文摘要:
Kinetic equations governing time evolution of positions and momenta of atoms in extended systems are derived using quantum-classical ensembles within the Non-Equilibrium Statistical Operator Method (NESOM). Ions are treated classically, while their electrons quantum mechanically; however, the statistical operator is not factorised in any way and no simplifying assumptions are made concerning the electronic subsystem. Using this method, we derive kinetic equations of motion for the classical degrees of freedom (atoms) which account fully for the interaction and energy exchange with the quantum variables (electrons). Our equations, alongside the usual Newtonian-like terms normally associated with the Ehrenfest dynamics, contain additional terms, proportional to the atoms velocities, which can be associated with the electronic friction. Possible ways of calculating the friction forces which are shown to be given via complicated non-equilibrium correlation functions, are discussed. In particular, we demonstrate that the correlation functions are directly related to the thermodynamic Matsubara Green's functions, and this relationship allows for the diagrammatic methods to be used in treating electron-electron interaction perturbatively when calculating the correlation functions. This work also generalises previous attempts, mostly based on model systems, of introducing the electronic friction into Molecular Dynamics equations of atoms.
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PDF链接:
https://arxiv.org/pdf/707.2988