On the relation between the magnitude and exponent of OTOCs
On the relation between the magnitude and exponent of OTOCs
复制标题
论OTOCs的大小与指数之间的关系
DOI：
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发表时间：
2018
影响因子：
5.4
通讯作者：
A. Kitaev
中科院分区：
文献类型：
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作者：
Yingfei Gu;A. Kitaev
我们导出了早期otoc的增长指数、指数前因子和第三个称为“分支时间”的数之间的恒等式。后者是在动态平均场框架内定义的，即根据延迟核。该恒等式可用于计算SYK和类似模型中的弦效应；在这个上下文中，我们还显式地定义了“字符串”。作为另一个应用，我们考虑一个SYK链。如果耦合强度β j大于一定阈值，忽略非线性（在OTOCs的大小上）效应，则蝴蝶波前的指数恰好为2π/β。
We derive an identity relating the growth exponent of early-time OTOCs, the pre-exponential factor, and a third number called “branching time”. The latter is defined within the dynamical mean-field framework, namely, in terms of the retarded kernel. This identity can be used to calculate stringy effects in the SYK and similar models; we also explicitly define “strings” in this context. As another application, we consider an SYK chain. If the coupling strength βJ is above a certain threshold and nonlinear (in the magnitude of OTOCs) effects are ignored, the exponent in the butterfly wavefront is exactly 2π/β.