自旋扩散与扩散分子动力学
Spin-Diffusions and Diffusive Molecular Dynamics
AI总结：
本文提出自旋扩散随机过程，将其与扩散分子动力学联系起来，探讨不同模型之间的关系及差异。
摘要：
介稳态凝聚态通常在飞秒时间尺度上围绕局部能量极小值波动，随后在纳秒或微秒内过渡到其他局部极小值。这巨大的尺度分离限制了经典分子动力学方法的应用，并催生了多种近似算法的发展。最近提出的一种方法是扩散分子动力学，旨在整合描述二元合金中两种物种占据概率的常微分方程，同时在准静态条件下演进化动位置。尽管扩散分子动力学显示出高效且与观察一致，但它本质上是一个模型，与经典分子动力学的联系尚不明确。在本文中，我们提出自旋扩散随机过程，并展示其如何与扩散分子动力学连接。自旋扩散模型将经典过阻尼兰格罕方程与二元合金物种间交换的动能蒙特卡罗模型耦合。在适当假设和近似下，自旋扩散可以显示导致扩散分子动力学类型模型。关键假设和近似包括明确的时间尺度分离、自旋交换速率的选择、低温近似以及平均场类型的近似。我们从不同假设推导出几种模型，并展示其与扩散分子动力学的关系。在简单的测试问题中探讨了这些模型之间的差异和相似性。
英文摘要：
Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive molecular dynamics which aims to integrate a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive molecular dynamics has shown to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical molecular dynamics. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive molecular dynamics. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive molecular molecular dynamics type models. The key assumptions and approximations include a well defined time scale separation, a choice of spin exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive molecular dynamics. Differences and similarities amongst the models are explored in a simple test problem.
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