论文标题
通过使用蒙特卡洛大都市解决运动方程：通过随机路径和最大口径原理的新方法
Solving equations of motion by using Monte Carlo Metropolis: Novel method via Random Paths and Maximum Caliber Principle
论文作者
论文摘要
物理和其他学科的永久挑战是解决部分微分方程，从而进行有益的调查是继续寻找新的程序。在这封信中，提出了一个新颖的蒙特卡洛大都市框架，用于解决拉格朗日系统中的运动方程。该实现在于通过使用最大能力原理获得的概率功能来对路径空间进行取样。将该方法应用于自由粒子和谐波振荡器问题，在这种问题中，从蒙特 - 卡洛模拟获得的数值平均路径以类似的方式收敛于从经典力学的分析解决方案，其中能量可以通过为每个系统的状态空间和计算每个系统的平均状态来最小化能量。因此，我们期望此过程足够通用，可以解决物理中的其他微分方程，并成为计算动态系统时间依赖性属性的有用工具，以了解统计机械系统的非平衡行为。
A permanent challenge in physics and other disciplines is to solve partial differential equations, thereby a beneficial investigation is to continue searching for new procedures to do it. In this Letter, a novel Monte-Carlo Metropolis framework is presented for solving the equations of motion in Lagrangian systems. The implementation lies in sampling the paths space with a probability functional obtained by using the maximum caliber principle. The methodology was applied to the free particle and the harmonic oscillator problems, where the numerically-averaged path obtained from the Monte-Carlo simulation converges to the analytical solution from classical mechanics, in an analogous way with a canonical system where energy is minimized by sampling the state space and computing the average state for each system. Thus, we expect that this procedure can be general enough to solve other differential equations in physics and to be a useful tool to calculate the time-dependent properties of dynamical systems in order to understand the non-equilibrium behavior of statistical mechanical systems.
