论文标题
通过外壳过程进行热化：小虚拟的优点
Thermalization by off-shell processes: the virtues of small virtuality
论文作者
论文摘要
我们研究了标量场$φ$耦合到其他两个标量场$χ_{1,2} $的热化，该量子在热平衡中构成浴缸。对于一系列质量，$φ$ opagator具有阈值和红外差异，在（准）粒子杆上消失了残留物，并消失了\ emph {on-shell}衰减速率，从而防止了$φ$平衡与浴缸的平衡。受量子开放系统理论的启发，我们获得了$φ$的降低密度矩阵的量子主方程，其中包括浴缸相关的时间依赖性，在放松动态方面产生了依赖时间的速率，并允许小虚拟过程$ \ propto $ \ propto $ \ propto $ \ propto 1/t t $ lonk Time t $ t $ t $ t $。尽管S-矩阵速率消失了，但这些\ emph {off-shell}过程导致热化。在阈值差异的情况下，我们发现热固定点的接近是$ e^{ - \ sqrt {t/t^*}} $，放松时间$ t^*$由于刺激的发射和吸收而在高温下变短。在红外情况下，将热固定点接近$ e^{ - γ（t）} $，其中$γ（t）$具有$ \ propto \ ln（t）$与$ t \ gg gg 1/t $的$ \ propto \ ln（t）$之间的交叉。在这种情况下，残留动力学中残留物和跨界的消失显然让人联想到重型杂质系统中的正交性灾难。结果通过虚拟过程获得了更多关于热化的一般课程。
We study the thermalization of a scalar field $Φ$ coupled to two other scalar fields $χ_{1,2}$ that constitute a bath in thermal equilibrium. For a range of masses the $Φ$ propagator features threshold and infrared divergences, a vanishing residue at the (quasi) particle pole and vanishing \emph{on-shell} decay rates thereby preventing the equilibration of $Φ$ with the bath via on-shell processes. Inspired by the theory of quantum open systems we obtain a quantum master equation for the reduced density matrix of $Φ$ that includes the time dependence of bath correlations, yielding time dependent rates in the dynamics of relaxation and allowing virtual processes of small virtuality $\propto 1/t$ at long time $t$. These \emph{off-shell} processes lead to thermalization despite vanishing S-matrix rates. In the case of threshold divergences we find that a thermal fixed point is approached as $e^{-\sqrt{t/t^*}}$ with the relaxation time $t^*$ becoming shorter at high temperature as a consequence of stimulated emission and absorption. In the infrared case, the thermal fixed point is approached as $e^{-γ(t)}$, where $γ(t)$ features a crossover between a $\propto \ln(t)$ and a $\propto t$ behavior for $t \gg 1/T$. The vanishing of the residue and the crossover in relaxational dynamics in this case is strikingly reminiscent of the orthogonality catastrophe in heavy impurity systems. The results yield more general lessons on thermalization via virtual processes.
