Nonequilibrium Relaxation Method

一种成熟的研究给定微观模型系统的热相和相变的模拟策略是所谓的平衡法，即首先实现有限系统的平衡系综，然后将结果外推到无限系统。这种平衡方法超越了热力学统计力学的标准理论，超越了热力学极限的概念。最近，在本研究项目首席研究员的倡议下，开发了另一种模拟策略，用于分析非平衡弛豫(NER)过程。它被称为NER方法。与平衡法相比，NER法具有一定的优势。NER方法提供了更简单的分析步骤。这意味着较少的系统误差，这在模拟中是不可避免的，并且提供了有效的资源利用。本课题研究的主要目的如下：(1)进一步发展NER方法。(2)改进了NER法作为研究材料性能的标准技术。(3)基于NER方法的分析仪软件的编写。在这个项目的四年时间里，实现了这三个目标。建立了用NER方法分析Kosterlitz-Thouless相变的方法，并以硬盘熔化为例，证明了两次KT相变。提出了粒子系统的无拒收蒙特卡罗方法，使高密度区域的模拟更加高效。设计了一个自动分析软件--NER分析器，并编写了部分代码。NER分析器使用NER方法分析相位和指数，方法是生成指定的仿真，对其进行仿真和分析，并在其数据库中生成准确的执行日志。

One well-established simulation strategy to study the thermal phases and transitions of a given microscopic model system is so-called the equilibrium method, in which one firstly realizes the equilibrium ensemble of a finite system and then extrapolates the results to infinite system. This equilibrium method traces over the standard theory of the thermal statistical mechanics, and over the idea of the thermodynamic limit. Recently, alternative simulation strategy has been developed by the initiative of the head investigator of this research project, which analyzes the nonequilibrium relaxation (NER) process. It is called the NER method. There are some advantages in the NER method over the equilibrium method. The NER method provides simpler analyzing procedure. This implies the less systematic error which is inevitable in the simulation and provides efficient resource usage. Main purpose of this research project is the following: (1) Further development of the NER method. (2) Refinement of the NER method as one standard technique to study material property. (3) Preparation towards analyzer software based on the NER method. During the four years of this project, these three are achieved. Analyzing method of the Kosterlitz-Thouless transition with the NER method is established, and it has turned out that hard-disk melting shows KT transition twice, as an example. Rejection free Monte Carlo method is developed for particle system, which makes simulation more efficient in high density region. An automatic analyzing software named as NER analyzer is designed and partly coded. The NER analyzer analyzes phase and exponent using the NER method by generating specified simulations, simulating and analyzing them, together with making precise log of execution in its database.