CANONICAL DYNAMICS - EQUILIBRIUM PHASE-SPACE DISTRIBUTIONS
CANONICAL DYNAMICS - EQUILIBRIUM PHASE-SPACE DISTRIBUTIONS
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DOI：
10.1103/physreva.31.1695
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发表时间：
1985-01-01
影响因子：
2.9
通讯作者：
HOOVER, WG
中科院分区：
文献类型：
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作者：
HOOVER, WG
诺塞修改了牛顿动力学，以便在N体系统的相空间中再现正则和等温等压概率密度。他这样做的缩放时间（与s）和距离（与V 1/D的D维）通过拉格朗日方程的运动。动力学方程描述的演变，这两个标度变量和他们的两个共轭动量p的s和pv。在这里，我们开发了一个略有不同的一组方程，免费的时间标度。我们在扩展相空间中找到了动力学稳态概率密度，其中x，px，V，ε今和ε n是变量，x是约化距离，ε今和ε n是热力学摩擦系数.我们发现这些摩擦系数具有高斯分布。从分布的小系统的非牛顿行为的程度可以估计。我们说明的动力学方程，考虑其应用到最简单的情况下，一维经典谐振子。
Nosé has modified Newtonian dynamics so as to reproduce both the canonical and the isothermal-isobaric probability densities in the phase space of an N-body system. He did this by scaling time (with s) and distance (with V 1/D in D dimensions) through Lagrangian equations of motion. The dynamical equations describe the evolution of these two scaling variables and their two conjugate momenta p s and p v. Here we develop a slightly different set of equations, free of time scaling. We find the dynamical steady-state probability density in an extended phase space with variables x, p x, V, ε̇, and ζ, where the x are reduced distances and the two variables ε̇ and ζ act as thermodynamic friction coefficients. We find that these friction coefficients have Gaussian distributions. From the distributions the extent of small-system non-Newtonian behavior can be estimated. We illustrate the dynamical equations by considering their application to the simplest possible case, a one-dimensional classical harmonic oscillator.