玻尔兹曼方程求解器适应于涌现的化学非平衡
Boltzmann Equation Solver Adapted to Emergent Chemical Non-equilibrium
AI总结：
本文提出一种新的方法求解空间均匀且各向同性的相对论玻尔兹曼方程，通过动态适应的正交多项式基集捕捉化学非平衡，验证了该方法的计算效率和对最终态化学非平衡的表示能力。
摘要：
我们提出了一种新的方法来求解空间均匀且各向同性的相对论玻尔兹曼方程。我们采用一组动态适应的正交多项式基集，以允许化学非平衡的出现。两个时间依赖的参数表征正交多项式集，即有效温度T(t)和相空间占据因子Υ(t)。在本文中，我们针对（有效）无质量费米子，推导出T(t)和Υ(t)的动力学方程，使得基集的零阶项单独捕获每种粒子分布的粒子数密度和能量密度。我们验证了该方法，并通过研究受早期宇宙中中微子冻结过程启发的模型问题，展示了该方法的计算效率以及表示最终态化学非平衡的能力。
英文摘要：
We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical non-equilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature $T(t)$ and phase space occupation factor $Υ(t)$. In this first paper we address (effectively) massless fermions and derive dynamical equations for $T(t)$ and $Υ(t)$ such that the zeroth order term of the basis alone captures the particle number density and energy density of each particle distribution. We validate our method and illustrate the reduced computational cost and the ability to easily represent final state chemical non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component ($e^\pm$-annihilation).
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