ShARK：相对论弛豫时间近似玻尔兹曼方程的随机输运框架

中文摘要 AI 辅助

我们证明了Anderson-Witting弛豫时间近似（相对论Bhatnagar-Gross-Krook（BGK）方程）作为随机N体粒子气体的N→∞极限出现，其中碰撞执行完全微正则动量重绘，在每次事件中强制局部能量-动量守恒。使用RAMBO算法采样洛伦兹不变相空间，我们推导了有限N单粒子动量谱，并表明随着局部粒子数增加，它收敛到Jüttner-Boltzmann平衡分布。我们将此弛豫核与平流-弛豫分裂方案耦合，构建了ShARK（随机平流弛豫动力学），一个用于弛豫时间近似玻尔兹曼方程的3D蒙特卡洛相对论求解器。该框架在概念上与格子玻尔兹曼方法相关，但在连续动量空间中表述，以避免远离局部平衡时有限阶动量离散化导致的精度损失。我们针对两个高度对称的共形膨胀，即Bjorken和Gubser流，将数值结果与分析解进行验证。该框架为远离平衡的相对论输运提供了第一性原理路径，应用范围从重离子碰撞到膨胀的天体物理等离子体。

英文摘要

We show that the Anderson-Witting relaxation-time approximation (relativistic Bhatnagar-Gross-Krook (BGK) equation) emerges as the $N\rightarrow \infty$ limit of a stochastic $N$-body particle gas, in which collisions perform a full microcanonical momentum redraw that enforces local energy-momentum conservation at every event. Using the RAMBO algorithm to sample the Lorentz-invariant phase space, we derive the finite-$N$ single-particle momentum spectrum and show that it converges to the Jüttner-Boltzmann equilibrium distribution as the local particle number grows. We couple this relaxation kernel to an advection-relaxation splitting scheme to construct ShARK (Stochastic Advection Relaxation Kinetics), a 3D Monte Carlo relativistic solver for the relaxation time approximation Boltzmann equation. The framework is conceptually related to lattice Boltzmann methods, but formulated in continuous momentum space to avoid the accuracy loss caused by finite-order momentum discretizations far from local equilibrium. We validate the numerical results against analytical solutions for two highly symmetric conformal expansions, the Bjorken and Gubser flows. The framework provides a first-principles route to far-from-equilibrium relativistic transport, with applications ranging from heavy-ion collisions to expanding astrophysical plasmas.

发表机构

• Departamento de Física, Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学物理系）
• Universidade Estadual de Campinas (Unicamp)（坎皮纳斯州立大学）

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58 pages, 13 figures