标题： 谱BBGKY：非线性玻尔兹曼和关联动力学的可扩展方案 显示英文标题

标题： Spectral BBGKY: a scalable scheme for nonlinear Boltzmann and correlation kinetics

摘要： 玻利乌布诺夫-博恩-格林-基尔克伍德-尤永（BBGKY）层次结构为描述多体系统的非平衡演化提供了一个时间反演对称的框架。 尽管基于玻尔兹曼的方法取得了成功，但系统地扩展到完整的非线性BBGKY层次结构仍然是一项主要挑战。 此外，即使在玻尔兹曼层面，准确处理非线性碰撞项仍然存在重大困难。 在这里，我们提出了谱BBGKY层次结构，这是传统BBGKY层次结构的一种解析等价且数值可处理的重新表述。 谱形式将原始的6n维相空间问题简化为坐标空间中谱系数的演化。 我们还开发了一种计算碰撞积分的解析方案，该方案实现了高精度，并消除了从相同初始状态进行重复随机演化时的系综平均需求。 该方案对于无质量粒子精确计算了完整的八重积分，而对于有质量粒子则将其简化为三重积分。 通过守恒定律分析、与解析解的比较、收敛性测试以及谱系数泄漏分析验证了谱BBGKY层次结构的有效性。 在最小截断情况下，谱BBGKY产生了一个谱非线性玻尔兹曼方程，其计算成本与线性化方法相当，同时能够捕捉完整的动力学。 当扩展到更高阶截断时，谱BBGKY层次结构提供了一个灵活的框架来研究多粒子关联。 这一框架提高了我们研究相对论重离子碰撞中早期热化之谜的能力，并阐明了流体力学在夸克-胶子等离子体演化极其早期阶段的适用性。 显示英文摘要

摘要： The Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy provides a time-reversal-symmetric framework for describing the nonequilibrium evolution of many-body systems. Despite the success of Boltzmann-based numerical approaches, systematically extending beyond this lowest-order truncation to the full nonlinear BBGKY hierarchy remains a major challenge. Moreover, even at the Boltzmann level, accurately treating the nonlinear collision term still presents significant difficulties. Here we propose the spectral BBGKY hierarchy, an analytically equivalent and numerically tractable reformulation of the conventional BBGKY hierarchy. The spectral formulation reduces the original 6n-dimensional phase-space problem to the evolution of spectral coefficients over the 3n-dimensional coordinate space. We also develop an analytic scheme for computing the collision integrals, which achieves high accuracy and removes the need for ensemble averaging over repeated stochastic evolutions from the same initial state. The scheme evaluates the full eight-fold integral exactly for massless particles, and reduces it to a three-fold one for massive particles. The validity of the spectral BBGKY hierarchy is verified through conservation law analysis, comparison with an analytical solution, convergence tests, and analysis of spectral coefficient leakage. At minimal truncation, the spectral BBGKY yields a spectral nonlinear Boltzmann equation that captures full dynamics with a computational cost comparable to that of linearized approaches. When extended to higher-order truncations, the spectral BBGKY hierarchy provides a flexible framework for studying multiparticle correlations. This framework advances our ability to investigate the early thermalization puzzle in relativistic heavy-ion collisions and to elucidate the applicability of hydrodynamics at remarkably early stages of quark-gluon plasma evolution.