Brownian Motion in AdS/CFT
Brownian Motion in AdS/CFT
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DOI：
10.1088/1126-6708/2009/07/094
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发表时间：
2008-12
期刊：
影响因子：
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通讯作者：
J. Boer;V. Hubeny;Mukund Rangamani;M. Shigemori
中科院分区：
文献类型：
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作者：
J. Boer;V. Hubeny;Mukund Rangamani;M. Shigemori
我们研究了AdS/CFT中的布朗运动和相应的Langevin方程。布朗粒子在大体积时空中被实现为渐近AdS黑洞背景中的探测基本弦，在AdS边界和视界之间伸展。弦上的模式被热黑洞环境激发，因此边界处的弦端点经历了不稳定的运动，这与边界CFT中表现出布朗运动的外部夸克相一致。半经典地，弦上的模式由于霍金辐射而被热激发，霍金辐射转化为边界朗之万方程中出现的随机力，而朗之万方程中的摩擦对应于被黑洞吸收的弦上的激发。给出了随机力和摩擦力的涨落耗散定理的一个整体证明。这项工作可以被视为理解流体-重力对应背后的量子微观物理学的一步。我们还开始研究的有效膜或拉伸视界图片的黑洞使用我们的大量布朗运动的描述的性质。
We study Brownian motion and the associated Langevin equation in AdS/CFT. The Brownian particle is realized in the bulk spacetime as a probe fundamental string in an asymptotically AdS black hole background, stretching between the AdS boundary and the horizon. The modes on the string are excited by the thermal black hole environment and consequently the string endpoint at the boundary undergoes an erratic motion, which is identified with an external quark in the boundary CFT exhibiting Brownian motion. Semiclassically, the modes on the string are thermally excited due to Hawking radiation, which translates into the random force appearing in the boundary Langevin equation, while the friction in the Langevin equation corresponds to the excitation on the string being absorbed by the black hole. We give a bulk proof of the fluctuation-dissipation theorem relating the random force and friction. This work can be regarded as a step toward understanding the quantum microphysics underlying the fluid-gravity correspondence. We also initiate a study of the properties of the effective membrane or stretched horizon picture of black holes using our bulk description of Brownian motion.