标题： 遍历等能分子动力学用于微正则系综平均值 显示英文标题

标题： Ergodic Isoenergetic Molecular Dynamics for Microcanonical-Ensemble Averages

摘要： 大量研究导致了遍历等温动力学，它可以为简单的（小的）动力学问题复制吉布斯的规范分布。 向哈密顿运动方程中添加一个或两个热浴力，可以为谐波振子、四次振子甚至“墨西哥帽”（双势阱）势能问题提供遍历等温动力学。 我们在这里考虑一种时间可逆的动力学方法，用于简单系统的吉布斯“微观正则”（等能）分布。 为了实现等能遍历性，我们在速度上偶尔添加随机旋转。 这个想法可以精确地保持能量，并且可以被设计成通过遍历动力学覆盖整个能量壳层。 我们完全避免了哈密顿混沌中典型的庞加莱截面孔洞和岛链。 我们用最简单的二维例子来说明这个想法，即一个粒子在一个周期性正方形晶格散射器阵列中运动，“单元模型”。 显示英文摘要

摘要： Considerable research has led to ergodic isothermal dynamics which can replicate Gibbs' canonical distribution for simple ( small ) dynamical problems. Adding one or two thermostat forces to the Hamiltonian motion equations can give an ergodic isothermal dynamics to a harmonic oscillator, to a quartic oscillator, and even to the "Mexican-Hat" ( double-well ) potential problem. We consider here a time-reversible dynamical approach to Gibbs' "microcanonical" ( isoenergetic ) distribution for simple systems. To enable isoenergetic ergodicity we add occasional random rotations to the velocities. This idea conserves energy exactly and can be made to cover the entire energy shell with an ergodic dynamics. We entirely avoid the Poincar\'e-section holes and island chains typical of Hamiltonian chaos. We illustrate this idea for the simplest possible two-dimensional example, a single particle moving in a periodic square-lattice array of scatterers, the "cell model".