Laird Brian B, Leimkuhler Benedict J
Department of Chemistry and Kansas Institute for Theoretical and Computational Science, University of Kansas, Lawrence, Kansas 66045, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jul;68(1 Pt 2):016704. doi: 10.1103/PhysRevE.68.016704. Epub 2003 Jul 29.
We demonstrate that the Nosé method for constant-temperature molecular-dynamics simulation [Mol. Phys. 52, 255 (1984)] can be substantially generalized by the addition of auxiliary variables to encompass an infinite variety of Hamiltonian thermostats. Such thermostats can be used to enhance ergodicity in systems, such as the one-dimensional harmonic oscillator or certain molecular systems, for which the standard Nosé-Hoover methods fail to reproduce converged canonical distributions. In this respect the method is similar in spirit to the method of Nosé-Hoover chains, but is both more general and Hamiltonian in structure (which allows for the use of efficient symplectic integration schemes). In particular, we show that, within the generalized Nosé formalism outlined herein, any Hamiltonian system can be thermostated with any other, including a copy of itself. This gives one an enormous flexibility in choosing the form of the thermostating bath. Numerical experiments are included in which a harmonic oscillator is thermostated with a collection of noninteracting harmonic oscillators as well as by a soft billiard system.
我们证明，通过添加辅助变量，恒温分子动力学模拟的Nosé方法[《分子物理学》52, 255 (1984)]可以得到实质性的推广，以涵盖无限多种哈密顿恒温器。这种恒温器可用于增强某些系统的遍历性，如一维谐振子或某些分子系统，对于这些系统，标准的Nosé - Hoover方法无法再现收敛的正则分布。在这方面，该方法在精神上与Nosé - Hoover链方法相似，但在结构上更具一般性且是哈密顿的（这允许使用高效的辛积分方案）。特别地，我们表明，在本文概述的广义Nosé形式体系内，任何哈密顿系统都可以用任何其他系统进行恒温控制，包括其自身的一个副本。这在选择恒温浴的形式方面给予了极大的灵活性。文中包含了数值实验，其中一个谐振子由一组非相互作用的谐振子以及一个软台球系统进行恒温控制。
