动态结构因子的相空间路径积分表示：强关联软球费米子的蒙特卡洛模拟
Phase space path integral representation of the dynamic structure factor. Monte Carlo simulation of strongly correlated soft-sphere fermions
AI总结：
本文利用 Wigner 路径积分蒙特卡洛方法计算强关联软球费米子的动态结构因子和径向分布函数，并揭示其峰结构与多重散射波干涉及 Anderson 局域化前兆效应的关系。
摘要：
动态结构因子（DSF）是一种数学函数，包含粒子间关联及其时间演化的信息。经典系统的 DSF 通常主要采用经典分子动力学进行计算。与此相反，本文研究的是量子系统及量子动态结构因子。利用量子力学的 Wigner 表述，基于 Wiener-Khinchin 定理（该定理表明随机路径的功率谱与其关联函数之间的关系），推导出了 DSF 的路径积分表示。作为一个有趣的物理实例，本文考虑了强关联软球费米子的 3D 量子系统。所发展的 Wigner 路径积分蒙特卡洛（WPIMC）方法已被用于在广泛的密度和温度范围内计算自旋分辨 DSF、径向分布函数（RDF）以及其他热力学函数。文中分析并解释了 RDF 和 DSF 上出现的峰的物理意义，这些峰源于交换相互作用和粒子间相互作用的干涉效应，以及多重散射之间的波干涉。在软球散射体系统中，这一现象可能是 Anderson 局域化的前兆效应，而 Anderson 局域化起源于多重散射路径之间的波干涉。
英文摘要：
The dynamic structure factor (DSF) is a mathematical function that contains information about inter-particle correlations and their time evolution. Mostly the classical molecular dynamics is used to calculate the DSF of the classical systems. On the contrary this article deals with quantum systems and the quantum dynamic structure factor. The Wigner formulation of quantum mechanics was used to derive the path integral representation of the DSF, which is based on the Wiener-Khinchin theorem showing relation of the the power spectrum of a random paths to their correlation function. The $3 {\rm D} $ quantum system of strongly correlated soft-sphere fermions was considered as an interesting physical example. The developed Wigner path integral Monte Carlo (WPIMC) approach has been developed to calculate the spin--resolved DSFs, the radial distribution functions (RDFs) and other thermodynamic functions in a wide range of density and temperatures. The physical meaning of the peaks arising on the RDFs and DSF have been analyzed and explained by the manifestation of the interference effects of the exchange and interparticle interactions and, as well as, the wave interference between multiple-scattering. This phenomenon in the system of the soft-sphere scatterers may to be the precursor effect of the Anderson localization, which finds its origin in the wave interference between multiple-scattering paths.
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