In this paper, we study how quantum correlation between subsystems changes in time by investigating time evolution of mutual information and logarithmic negativity in two protocols of mass quench. Hamiltonian in both protocols is for 2-dimensional free scalar theory with time-dependent mass: the mass in one case decreases monotonically and vanishes asymptotically (ECP), and that in the other decreases monotonically before t = 0, but increases monotonically afterward, and becomes constant asymptotically (CCP). We study the time evolution of the quantum correlations under those protocols in two different limits of the mass quench; fast limit and slow limit depending on the speed with which the mass is changed. We obtain the following two results: (1) For the ECP, we find that the time evolution of logarithmic negativity is, when the distance between the two subsystems is large enough, well-interpreted in terms of the propagation of relativistic particles created at a time determined by the limit of the quench we take. On the other hand, the evolution of mutual information in the ECP depends not only on the relativistic particles but also on slowly-moving particles. (2) For the CCP, both logarithmic negativity and mutual information oscillate in time after the quench. When the subsystems are well-separated, the oscillation of the quantum correlations in the fast limit is suppressed, and the time evolution looks similar to that under the ECP in the fast limit.

中文翻译：

---

平滑淬火中对数负性和互信息的动力学

在本文中，我们通过研究两种质量淬灭协议中互信息和对数负性的时间演化来研究子系统之间的量子相关性如何随时间变化。两种协议中的哈密顿量均适用于具有时间相关质量的二维自由标量理论：一种情况下的质量单调减少并渐近消失 (ECP)，另一种情况下的质量在 t = 0 之前单调减少，但之后单调增加，并且渐近变为常数 (CCP)。我们研究了在质量淬灭的两个不同限制下这些协议下量子相关性的时间演变；快限和慢限取决于质量变化的速度。我们得到以下两个结果： (1) 对于 ECP，我们发现对数负的时间演化是，当两个子系统之间的距离足够大时，就可以很好地解释相对论粒子的传播，这种传播是由我们采用的淬火极限决定的。另一方面，ECP 中互信息的演化不仅依赖于相对论粒子，还依赖于缓慢移动的粒子。(2) 对于 CCP，对数负性和互信息在淬火后都随时间振荡。当子系统分离良好时，快速极限下的量子关联振荡受到抑制，时间演化与快速极限下的 ECP 下的演化相似。ECP 中互信息的演化不仅依赖于相对论粒子，还依赖于缓慢移动的粒子。(2) 对于 CCP，对数负性和互信息在淬火后都随时间振荡。当子系统分离良好时，快速极限下的量子关联振荡受到抑制，时间演化与快速极限下的 ECP 下的演化相似。ECP 中互信息的演化不仅依赖于相对论粒子，还依赖于缓慢移动的粒子。(2) 对于 CCP，对数负性和互信息在淬火后都随时间振荡。当子系统分离良好时，快速极限下的量子关联振荡受到抑制，时间演化与快速极限下的 ECP 下的演化相似。