大$q$ SYK模型中的“瞬时热化”意味着什么？
What does "instant thermalization" in large-$q$ SYK models mean?
- Jožef Stefan Institute（约泽夫·斯特凡研究所）
- Gesellschaft für wissenschaftliche Datenverarbeitung mbH Göttingen (GWDG)（哥廷根科学数据处理有限公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过解析和数值计算，揭示大$q$ SYK模型中瞬时热化仅存在于正时间块，有效温度受非对角块限制，速率为$\Gamma \sim T q^{-1}$。
AI中文摘要：
受双体相互作用SYK模型中观测到的普朗克热化速率$\Gamma \sim T$的启发，我们研究了$q/2$体情形下的热化。先前对此类系统的研究确立了在$1/q$领头阶下瞬时热化的概念。曾有猜想认为热化可能仍是普朗克型的，但具有发散速率$\Gamma \sim T q$，这解释了“瞬时”部分。对于一个解析和数值上可处理的系统，我们计算了在时间$t = 0$淬火后的有效温度，确实发现了普朗克速率，但具有意外的衰减行为$\Gamma \sim T q^{-1}$。这与因果格林函数$\mathcal{G}(t_1, t_2)$的行为形成对比，后者在双时间平面块$t_1, t_2 > 0$内立即获得热形式。由此得出的图景是，瞬时热化仅对该块有意义，而对角线外的块$t_1 \cdot t_2 < 0$在任何$q$下本质上都是非热的。由于有效温度是从跨越所有块的关联中获得的，它继承了由非对角块设定的有限速率。我们通过直接研究非热关联的时间依赖性来阐明这一点。
英文摘要：
Motivated by the Planckian thermalization rate $Γ\sim T$ observed in the two-body interacting SYK model, we study thermalization in the $q/2$-body case. Previous studies of such systems have established the notion of instantaneous thermalization to leading order in $1/q$. It was conjectured that the thermalization may still be Planckian but with a divergent rate $Γ\sim T q$, explaining the ``instantaneous'' part. For an analytically and numerically tractable system, we calculate the effective temperatures after a quench at time $t = 0$ and indeed find a Planckian rate, albeit with the unexpected decaying behavior $Γ\sim T q^{-1} $. This is contrasted with the behavior of the causal Green's function $\mathcal{G}(t_1, t_2)$, which instantly acquires a thermal form in the two-time plane block $t_1, t_2 > 0$. The resulting picture is that instant thermalization is a meaningful concept only for this block, while the off-diagonal blocks $t_1 \cdot t_2 < 0$ are inherently non-thermal at any $q$. Since the effective temperature is obtained from correlations spanning all blocks, it inherits a finite rate set by the off-diagonal. We illustrate this directly by studying the non-thermal correlations' time dependence.
