We present an analytic solution of a simple set of equations that govern the expansion of boost-invariant plasmas of massless particles. These equations describe, approximately, the early time, collisionless regime, and the transition to hydrodynamics at late time. Their mathematical structure encompasses all versions of second order hydrodynamics when applied to Bjorken flows. The analytic solution provides an explicit expression for the attractor solution that connects the collisionless regime to hydrodynamics. It also constitutes a neat example of an application of the theory of resurgence in asymptotic series.

中文翻译：

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Bjorken 流的解析吸引子

我们提出了一组简单方程的解析解，这些方程控制无质量粒子的增强不变等离子体的膨胀。这些方程大致描述了早期、无碰撞状态和后期向流体动力学的过渡。当应用于 Bjorken 流时，它们的数学结构包含所有版本的二阶流体动力学。解析解为将无碰撞状态与流体动力学连接起来的吸引子解提供了明确的表达式。它还构成了在渐近级数中应用复兴理论的一个巧妙例子。