在GJF恒温器中定义精确的动力学统计速度
Defining velocities for accurate kinetic statistics in the GJF thermostat
摘要：
我们扩大了两个以前的发展离散时间Langevin系统的建模。一个是有据可查的Grønbech-Jensen Farago（GJF）恒温器，它已被证明可以提供相空间的鲁棒和准确的配置采样。另一个是最近的发现，动力学也可以准确采样的GJF方法。通过对所有可能的有限差分近似速度的全面调查，我们得出两个主要结论：~1）不可能定义一个所谓的现场速度，使得动力学温度将是正确的和独立的时间步长，和~2）存在一组无限多的可能性，定义一个两点（蛙跳）的速度，除了从GJF算法获得的正确的构型统计正确的措施动能的线性系统。我们给出明确的表达式可能的定义，我们将这些到方便和实用的算法形式的正常Verlet型算法，以及一组建议的标准，选择一个有用的定义速度。
英文摘要：
We expand on two previous developments in the modeling of discrete-time Langevin systems. One is the well-documented Grønbech-Jensen Farago (GJF) thermostat, which has been demonstrated to give robust and accurate configurational sampling of the phase space. Another is the recent discovery that also kinetics can be accurately sampled for the GJF method. Through a complete investigation of all possible finite difference approximations to the velocity, we arrive at two main conclusions:~1) It is not possible to define a so-called on-site velocity such that kinetic temperature will be correct and independent of the time step, and~2) there exists a set of infinitely many possibilities for defining a two-point (leap-frog) velocity that measures kinetic energy correctly for linear systems in addition to the correct configurational statistics obtained from the GJF algorithm. We give explicit expressions for the possible definitions, and we incorporate these into convenient and practical algorithmic forms of the normal Verlet-type algorithms along with a set of suggested criteria for selecting a useful definition of velocity.
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