论文标题
$ λϕ^4 $理论在扩展的宇宙中的远程平衡动力学
Far-from-equilibrium kinetic dynamics of $λϕ^4$ theory in an expanding universe
论文作者
论文摘要
我们研究了Friedmann-Lemaitre-Robertson-Walker-Walker SpaceTime中具有四重奏（树级）自我相互作用的无质量标量粒子粒子的气体（树级）自我相互作用（$ λϕ^4 $）的气体的玻璃体方程的远程平衡行为。使用新的协变生函数在Boltzmann分布函数的矩中，我们通过分析确定频谱的子集和线性化Boltzmann碰撞运算符的相应特征函数。我们展示了如何使用协变量生成函数来在整个非线性方案中找到矩的精确方程。与硬球的超偏移性气体的情况不同（总横截面是恒定的），$ λϕ^4 $，横截面随能量减小的事实暗示了任意高阶的矩直接将其直接二成到低阶矩。提出了标量场情况的数值溶液，并将其与硬球气体的数值溶液进行了比较。
We investigate the far-from-equilibrium behavior of the Boltzmann equation for a gas of massless scalar field particles with quartic (tree level) self-interactions ($λϕ^4$) in Friedmann-Lemaitre-Robertson-Walker spacetime. Using a new covariant generating function for the moments of the Boltzmann distribution function, we analytically determine a subset of the spectrum and the corresponding eigenfunctions of the linearized Boltzmann collision operator. We show how the covariant generating function can be also used to find the exact equations for the moments in the full nonlinear regime. Different than the case of a ultrarelativistic gas of hard spheres (where the total cross section is constant), for $λϕ^4$ the fact that the cross section decreases with energy implies that moments of arbitrarily high order directly couple to low order moments. Numerical solutions for the scalar field case are presented and compared to those found for a gas of hard spheres.
