标题： 远离平衡态的动力学在膨胀宇宙中的$λφ^4$理论 显示英文标题

标题： Far-from-equilibrium kinetic dynamics of $λφ^4$ theory in an expanding universe

摘要： 我们研究了Friedmann-Lemaître-Robertson-Walker时空下具有四次（树级）自相互作用（$\lambda \phi^4$）的质量less标量场粒子气体的远离平衡态的Boltzmann方程行为。 利用Boltzmann分布函数矩的一个新的协变生成函数，我们解析地确定了线性化Boltzmann碰撞算符谱的一个子集及其对应的特征函数。我们展示了如何使用该协变生成函数来找到全非线性情形下的矩的精确方程。 与硬球超相对论气体的情况不同（其中总截面是常数），对于$\lambda \phi^4$，截面随能量减小的事实意味着任意高阶矩直接耦合到低阶矩。 标量场情形的数值解被给出并与硬球气体的情形进行了比较。 显示英文摘要

摘要： 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 ($\lambda \phi^4$) 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 $\lambda \phi^4$ 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.