从软模式角度理解非阿贝尔规范理论的热化
Understanding thermalization in a non-Abelian gauge theory in terms of its soft modes
AI总结：
本文使用从头算格点技术测量了SU(2)规范理论中软模式在平衡与非平衡态下的最大李雅普诺夫指数，发现系统表现出混沌特征，并首次在解禁闭相变附近测量了临界模式的指数。
摘要：
我们使用从头算格点技术，测量了在热平衡和非平衡条件下，由软动量模式组成的SU(2)规范理论中物理态的最大李雅普诺夫指数$λ_L$。我们实现了不同的算法，以恰当地描述软模式在广泛温度范围和非平衡条件下的动力学。非平衡态是通过为低动量软胶子设定过占据的初始条件来实现的，而热态则由强相互作用的软胶子组成，在这些温度下，它们与硬动量模式很好地分离。在这两种状态下都观察到了正李雅普诺夫指数谱，类似于混沌动力系统。根据以该谱衡量的Kolmogorov-Sinai熵率，我们估计在$T\sim 600$ MeV下，从非热态开始实现热化的典型时间尺度为$\sim 0.50(3)$ fm/c。我们还首次使用经典$Z_2$标量场理论的非时序关联子，测量了SU(2)长波长临界模式的$λ_L$，该理论与SU(2)共享相同的普适行为，测量在解禁闭相变附近进行。观察到$λ_L$在转变温度处达到最大值。
英文摘要：
We measure the maximal Lyapunov exponent $λ_L$ of physical states in a SU(2) gauge theory consisting of soft momentum modes both in and out-of-thermal equilibrium conditions using ab-initio lattice techniques. We have implemented different algorithms to appropriately describe the dynamics of soft-modes for a wide range of temperatures and under non-equilibrium conditions. The non-equilibrium state has been realized starting from an over-occupied initial condition for low momentum soft gluons whereas the thermal state comprises of strongly interacting soft gluons at temperatures where these are well separated from the hard momentum modes. Spectra of positive Lyapunov exponents is observed in both these states, similar to a chaotic dynamical system. From the Kolmogorov-Sinai entropy rate measured in terms of this spectrum, we estimate a typical time-scale of $\sim 0.50(3)$ fm/c to achieve thermalization at $T\sim 600$ MeV starting from the non-thermal state. We also measure, for the first time, the $λ_L$ for long wavelength critical modes of SU(2) using the out-of-time-ordered correlator of a classical $Z_2$ scalar field theory, which shares the same universal behavior with SU(2), near the deconfinement phase transition. The $λ_L$ is observed to maximize at the transition temperature.
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