量子湍流是一种以高度非线性为特征的远离平衡过程。全息对偶提供了一个系统性框架，通过在(4+1)维黑洞背景中数值求解对偶的Abelian-Higgs理论，来模拟衰减的(3+1)维量子湍流。我们揭示了总涡旋线密度L会出现不同类型的衰减行为，具体取决于初始涡旋线密度，范围从L∼t^{-1.5}到L∼t^{-1}，类似于Phys. Rev. Lett. 96, 035301 (2006)中对^3He的实验观测，以及Phys. Rev. Lett. 82, 4831 (1999)和Phys. Rev. Lett. 118, 134501 (2017)中对^4He的实验观测。此外，通过测量黑洞视界处的能量通量，我们确定能量耗散率dE/dt与总涡旋线密度的平方成正比，这与W. F. Vinen提出的涡旋线衰减方程以及Nature Physics 7, 473-476 (2011)中的实验测量结果一致。
英文摘要：
Quantum turbulence is a far-from-equilibrium process characterized by high nonlinearity. Holographic duality provides a systematic framework for simulating the decaying $(3+1)$-dimensional quantum turbulence by numerically solving the dual Abelian-Higgs theory in a $(4+1)$-dimensional black hole background. We reveal that different types of decay behavior of the total vortex line density $L$ emerge depending on the initial vortex line density, ranging from $L\sim t^{-1.5}$ to $L\sim t^{-1}$, similar to the experimental observation of $^3$He in Phys. Rev. Lett. 96, 035301 (2006), and of $^4$He in Phys. Rev. Lett. 82, 4831 (1999) and in Phys. Rev. Lett. 118, 134501 (2017). Furthermore, by measuring the energy flux at the black hole horizon, we determine that the energy dissipation rate $dE/dt$ is proportional to the square of the total vortex line density, consistent with the vortex line decay equation proposed by W. F. Vinen and also the experimental measurement in Nature Physics 7, 473 - 476 (2011).
Ultraviolet dissipation and defect OPE in bottom-up holographic interfaces
Weinberg Institute for Theoretical Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校温伯格理论物理研究所）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo（东京大学 Kavli宇宙物理与数学研究所（WPI），东京大学高等研究院）
Holographic Turbulence and Numerical Estimate of the Fractal Dimension of the Turbulent Horizon
University of Chinese Academy of Sciences（中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Beijing Normal University（北京师范大学）
On Functional and Holographic Renormalization Group Methods in Stochastic Theory of Turbulence
A nonlocal quantum-field model is constructed for the system of hydrodynamic equations for incompressible viscous fluid (the stochastic Navier--Stokes (NS) equation and the continuity equation). This model is studied by the following two mutually parallel methods: the Wilson--Polchinski functional renormalization group method (FRG), which is based on the exact functional equation for the generating functional of amputated connected Green's functions (ACGF), and the Heemskerk--Polchinski holographic renormalization group method (HRG), which is based on the functional Hamilton--Jacobi (HJ) equat…
