关于AdS $_2$扩散边界的普适性和线性化流体力学的破裂
On the universality of AdS$_2$ diffusion bounds and the breakdown of linearized hydrodynamics
摘要：
对强耦合系统和全息模型中扩散系数的普遍边界的追求有着悠久的历史。一个通用的速度尺度的识别，独立的定义明确的准粒子激发的存在下，是这个程序的主要挑战之一。最近的一项分析，有效的紧急红外固定点表现出当地的量子临界性，双红外AdS $_2$几何形状，建议确定这样的速度使用的时间和长度尺度，在流体力学打破-平衡速度。后者涉及的流体动力学扩张的收敛半径，它是从一个流体动力学扩散模式和一个非流体动力学模式之间的碰撞与IR AdS $_2$区域相关联提取。在这个简短的说明中，我们证实了这一图片的全息系统显示自发打破平移不变性。此外，我们发现，在零温度下，由量子混沌和因果关系和流体动力学定义的上限的下限完全一致，唯一确定的扩散常数。最后，我们评论的意义和普遍性，这一新提出的处方。
英文摘要：
The chase of universal bounds on diffusivities in strongly coupled systems and holographic models has a long track record. The identification of a universal velocity scale, independent of the presence of well-defined quasiparticle excitations, is one of the major challenges of this program. A recent analysis, valid for emergent IR fixed points exhibiting local quantum criticality, and dual to IR AdS$_2$ geometries, suggests to identify such a velocity using the time and length scales at which hydrodynamics breaks down -- the equilibration velocity. The latter relates to the radius of convergence of the hydrodynamic expansion and it is extracted from a collision between a hydrodynamic diffusive mode and a non-hydrodynamic mode associated to the IR AdS$_2$ region. In this short note, we confirm this picture for holographic systems displaying the spontaneous breaking of translational invariance. Moreover, we find that, at zero temperature, the lower bound set by quantum chaos and the upper one defined by causality and hydrodynamics exactly coincide, determining uniquely the diffusion constant. Finally, we comment on the meaning and universality of this newly proposed prescription.
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