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Semiclassical modeling of quantum-mechanical multiparticle systems using parallel particle-in-cell methods.

机译：使用并行单元格内粒子方法的量子力学多粒子系统的半经典建模。

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摘要

We are successful in building a code that models many particle dynamic quantum systems by combining a semiclassical approximation of Feynman path integrals with parallel computing techniques (particle-in-cell) and numerical methods developed for simulating plasmas, establishing this approach as a viable technique for multiparticle time-dependent quantum mechanics. Run on high-performance parallel computers, this code applies semiclassical methods to simulate the time evolution of wavefunctions of many particles. We describe the analytical derivation and computational implementation of these techniques in detail. We present a study to thoroughly demonstrate the code's fidelity to quantum mechanics, resulting in innovative visualization and analysis techniques. We introduce and exhibit a method to address fermion particle statistics. We present studies of two quantum-mechanical problems: a two-electron, one-dimensional atom, resulting in high-quality extractions of one- and two-electron eigenstates, and electrostatic quasi-modes due to quantum effects in a hot electron plasma, relevant for predictions about stellar evolution. We supply discussions of alternative derivations, alternative implementations of the derivations, and an exploration of their consequences. Source code is shown throughout this dissertation. Finally, we present an extensive discussion of applications and extrapolations of this work, with suggestions for future direction.
机译：我们成功地建立了一个模型，通过将费曼路径积分的半经典近似与并行计算技术（单元中的粒子）和为模拟等离子体而开发的数值方法相结合，建立了一种对许多粒子动态量子系统进行建模的代码，从而将该方法确立为可行的方法多粒子时间相关的量子力学。该代码在高性能并行计算机上运行，​​应用半经典方法来模拟许多粒子的波函数的时间演化。我们将详细描述这些技术的解析推导和计算实现。我们提出一项研究，以彻底证明代码对量子力学的忠诚度，从而产生了创新的可视化和分析技术。我们介绍并展示了一种解决费米子粒子统计数据的方法。我们目前对两个量子力学问题进行研究：一个两电子一维原子，导致高质量的一电子和二电子本征态提取，以及由于热电子等离子体中的量子效应而导致的静电准模，与有关恒星演化的预测有关。我们提供有关替代派生，派生的替代实现以及对它们的后果的探讨的讨论。全文中均显示了源代码。最后，我们对这项工作的应用和推断进行了广泛的讨论，并提出了未来的建议。

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