论文标题
流体动力扩散及其在广告附近的崩溃$ _2 $量子关键点
Hydrodynamic diffusion and its breakdown near AdS$_2$ quantum critical points
论文作者
论文摘要
流体动力学提供了足够长的时间和波长相互作用的量子场理论的普遍描述，但根据该理论的显微镜细节而分解。在量子关键点附近，预计动力学的某些方面是通用的，并由临界点的性质决定。我们使用仪表重力二元性来研究两个低温状态在两个低温状态的扩散流体动力学的分解，并用ADS $ _2 $地平线进行了二重孔，它们在时间上表现出量子临界动力学，并在时间上表现出紧急的缩放对称性。我们发现，分解的特征是智障绿色功能的扩散极与与ADS $ _2 $几何区域相关的极点之间发生碰撞，因此局部平衡时间是由理论的Infra-Red属性设置的。碰撞时频率和波形的绝对值（$ω_{eq} $和$ k_ {eq} $）提供了所有低温扩散性$ d $ d $ d $ d $ d $ d =ω__{eq}/k_ {eq}/k_ {eq}^2 $ sception $ d $ pecody的自然表征$δ$的基础量子批判理论的操作员。我们确认在SYK链模型中也满足了这些关系的强烈相互作用。我们的工作为对量子关键阶段的运输有更深入的了解铺平了道路。
Hydrodynamics provides a universal description of interacting quantum field theories at sufficiently long times and wavelengths, but breaks down at scales dependent on microscopic details of the theory. In the vicinity of a quantum critical point, it is expected that some aspects of the dynamics are universal and dictated by properties of the critical point. We use gauge-gravity duality to investigate the breakdown of diffusive hydrodynamics in two low temperature states dual to black holes with AdS$_2$ horizons, which exhibit quantum critical dynamics with an emergent scaling symmetry in time. We find that the breakdown is characterized by a collision between the diffusive pole of the retarded Green's function with a pole associated to the AdS$_2$ region of the geometry, such that the local equilibration time is set by infra-red properties of the theory. The absolute values of the frequency and wavevector at the collision ($ω_{eq}$ and $k_{eq}$) provide a natural characterization of all the low temperature diffusivities $D$ of the states via $D=ω_{eq}/k_{eq}^2$ where $ω_{eq}=2πΔT$ is set by the temperature $T$ and the scaling dimension $Δ$ of an operator of the infra-red quantum critical theory. We confirm that these relations are also satisfied in an SYK chain model in the limit of strong interactions. Our work paves the way towards a deeper understanding of transport in quantum critical phases.
