Many-body chaos and energy dynamics in holography
Many-body chaos and energy dynamics in holography
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DOI：
10.1007/jhep10(2018)035
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发表时间：
2018-09
影响因子：
5.4
通讯作者：
Mike Blake;R. Davison;S. Grozdanov;Hong Liu
中科院分区：
文献类型：
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作者：
Mike Blake;R. Davison;S. Grozdanov;Hong Liu
最近的研究表明，除了超时有序相关函数（OTOCs）之外，量子混沌也在热能量密度两点函数中有明显的表现，至少对于最大混沌系统是这样。这种表现形式，被称为跳极，涉及在复频率和动量平面上围绕一个特殊点ω= λ, k= λ/v B的能量密度两点函数的解析行为。这里λ和v B是表征量子混沌的李雅普诺夫指数和蝴蝶速度。本文给出了一个论据，证明了跳极现象对于一般有限温度对偶爱因斯坦引力与物质耦合的系统是普遍存在的。在这样做的过程中，我们发现了围绕静态黑洞几何的线性化爱因斯坦方程的一个令人惊讶的普遍特征。我们还分析地研究了一个全息轴子模型，在这个模型中，我们的一般论点的所有特征以及跳极现象都可以得到详细的验证。
Recent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density two-point functions, at least for maximally chaotic systems. The manifestation, referred to as pole-skipping, concerns the analytic behaviour of energy density two-point functions around a special point ω= iλ, k= iλ/v B in the complex frequency and momentum plane. Here λ and v B are the Lyapunov exponent and butterfly velocity characterising quantum chaos. In this paper we provide an argument that the phenomenon of pole-skipping is universal for general finite temperature systems dual to Einstein gravity coupled to matter. In doing so we uncover a surprising universal feature of the linearised Einstein equations around a static black hole geometry. We also study analytically a holographic axion model where all of the features of our general argument as well as the pole-skipping phenomenon can be verified in detail.