论文标题
TODA链的可整合流体动力学：小型系统的情况
Integrable hydrodynamics of Toda chain: case of small systems
论文作者
论文摘要
从具有多个自由度的微观离散晶格系统转到了一些粗粒粒度方程式描述的介质连续体系统是一项挑战。常见的民间传说是采用热力学极限，以便离散晶格的物理学描述了连续性结果。这样做的分析程序依赖于定义较小的长度尺度（通常是晶格间距）来粗粒显微镜进化方程。然后，从微观量表转移到介质量表需要仔细的近似值。在这项工作中，我们通过数值测试TODA链中的粗化，这是一个可相互作用的集成系统，即具有宏观数量保守电荷的系统。具体而言，我们通过使用三种不同的方法计算时空热相关性来研究波动的扩散：（a）使用微观分子动力学模拟使用大量粒子； （b）解决广义流体动力学方程； （c）求解每个保守量的线性欧拉尺度方程。令人惊讶的是，小型系统的结果（C）与宏观系统的热力学结果相匹配（a）和（b）。这重申了可整合流体动力学在描述实验室中的实验的重要性和有效性，在该实验室中，我们通常具有微观系统。
Passing from a microscopic discrete lattice system with many degrees of freedom to a mesoscopic continuum system described by a few coarse-grained equations is challenging. The common folklore is to take the thermodynamic limit so that the physics of the discrete lattice describes the continuum results. The analytical procedure to do so relies on defining a small length scale (typically the lattice spacing) to coarse-grain the microscopic evolution equations. Moving from the microscopic scale to the mesoscopic scale then requires careful approximations. In this work, we numerically test the coarsening in a Toda chain, which is an interacting integrable system, i.e. a system with a macroscopic number of conserved charges. Specifically, we study the spreading of fluctuations by computing the spatiotemporal thermal correlations with three different methods: (a) Using microscopic molecular dynamics simulation with a large number of particles; (b) solving the generalized hydrodynamics equation; (c) solving the linear Euler scale equations for each conserved quantities. Surprisingly, the results for the small systems (c) match the thermodynamic results in (a) and (b) for macroscopic systems. This reiterates the importance and validity of integrable hydrodynamics in describing experiments in the laboratory, where we typically have microscopic systems.
