零质量约束动力学下的绝热运动和统计力学
Adiabatic motion and statistical mechanics via mass zero constrained dynamics
摘要：
在最近的工作中[Coretti等人，The Journal of化学物理，2018，149，191102]，提出了一种数值求解壳模型极化动力学的新算法。该方法，广泛适用于系统，涉及分离的动力学变量，采用约束分子动力学严格执行的条件下，在快速的自由度上的力，建模为零质量，在每个时间步为零。该算法是辛的和完全时间可逆的，并导致稳定和有效的传播。在本文中，我们完成了零质量约束动力学力学的讨论，通过展示如何使其适应的问题，快速的自由度必须满足附加条件。这种扩展包括，特别是，第一原理分子动力学的重要情况。然后，我们考虑的质量为零的约束动力系统的统计力学证明，在物理相空间中的动态采样的边缘概率恢复的形式的Born-Oppenheimer概率密度。
英文摘要：
In recent work [Coretti et al., The Journal of Chemical Physics, 2018, 149, 191102], a new algorithm to solve numerically the dynamics of the shell model for polarization was presented. The approach, broadly applicable to systems involving adiabatically separated dynamical variables, employs constrained molecular dynamics to strictly enforce the condition that the force on the fast degrees of freedom, modeled as having zero mass, is null at each time step. The algorithm is symplectic and fully time reversible, and results in stable and efficient propagation. In this paper we complete the discussion of the mechanics of mass zero constrained dynamics by showing how to adapt it to problems where the fast degrees of freedom must satisfy additional conditions. This extension includes, in particular, the important case of first principles molecular dynamics. We then consider the statistical mechanics of the mass zero constrained dynamical system demonstrating that the marginal probability sampled by the dynamics in the physical phase space recovers the form of the Born-Oppenheimer probability density.
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