有限温度下线性谐振子晶格的分子动力学模拟

刘白伊郦; 唐少强

doi:10.3879/j.issn.1000-0887.2015.01.005

有限温度下线性谐振子晶格的分子动力学模拟

doi: 10.3879/j.issn.1000-0887.2015.01.005

北京大学应用物理与技术研究中心;北京大学工学院, 北京 100871

基金项目: 国家自然科学基金(11272009)

详细信息

作者简介:
刘白伊郦(1991—)，女，四川人，博士生（E-mail: lbyili@pku.edu.cn）；唐少强(1970—)，男，江苏苏州人，教授(通讯作者. E-mail: maotang@pku.edu.cn).

中图分类号: O39
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出版历程
- 收稿日期: 2014-09-24
- 修回日期: 2014-11-02
- 刊出日期: 2015-01-15

Molecular Dynamics Simulation of Linear Harmonic Lattices at Finite Temperature

CAPT of Peking University; College of Engineering, Peking University, Beijing 100871, P.R.China

Funds: The National Natural Science Foundation of China(11272009)

摘要

摘要: 基于双向界面条件和声子热浴，提出了一种新的热流输入方法，该方法未引入任何耗散因子或经验参数，能在局域的空间和时间上实现有限温度下的原子模拟.对于一维线性谐振子晶格，采用双向界面条件作为系统的边界，目的是为了让热流能从外界输入系统，同时允许内部的波动自由地传出，从而实现系统中能量的动态平衡.通过数值计算发现，双向界面条件能让正方向的波完整地输入，同时还能抑制反方向的波的输入，因此，边界条件可以起到行波的二极管的作用.声子热浴的正则模态能很好地描述原子的热振动，通过推导可将正则模态分解为正方向和反方向的输入波，取正方向的波来构造热源项.数值算例表明，热流输入方法对于线性谐振子链非常有效，系统能快速地达到预期的温度，并且能够维持在稳定的状态，同时，还能很好地处理有限温度下的非热运动.
- 热流输入 /
- 有限温度 /
- 原子模拟 /
- 谐振子晶格
Abstract: A heat jet approach for atomic simulation at finite temperature in both local space and time was proposed based on the 2-way boundary condition and phonon heat bath, without any dissipation factor and empirical parameter introduced. A subsystem was extracted from a space lattice for analysis of the exact molecular dynamics lest the entire lattice was to be solved numerically. For an extracted linear harmonic chain, the 2-way boundary condition allowed effective incoming waves fully enter the subsystem, and meanwhile, non-thermal motion and thermal fluctuation propagate freely out of the subsystem, to realize dynamic equilibrium of the system energy. During numerical calculation, the 2-way boundary condition worked like a wave diode which let in the positive-going waves while keeping out the negative-going ones. The normal mode of phonon heat bath well described the atomic heat vibration, then it was decoupled into positive-going and negative-going input waves of which the former was used to build the heat source term. For the molecular dynamics simulation of linear harmonic chains, the numerical tests demonstrate effectiveness of the proposed heat jet approach, which makes the chain rapidly reach the expectant temperature, keeps it in a steady state thereafter, and reasonably depicted the additional non-thermal atomic motion at finite temperature.
- heat jet /
- finite temperature /
- atomic simulation /
- harmonic lattice

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