Hydrodynamic theory of two-dimensional incompressible polar active fluids with quenched and annealed disorder.
Hydrodynamic theory of two-dimensional incompressible polar active fluids with quenched and annealed disorder.
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DOI：
10.1103/physreve.106.044608
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
Leiming Chen;Chiu Fan Lee;A. Maitra;J. Toner
中科院分区：
文献类型：
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作者：
Leiming Chen;Chiu Fan Lee;A. Maitra;J. Toner
我们研究了二维（2D）不可压缩极性活性流体在淬火和退火无序的存在下的运动相。我们表明，长程极序持续存在，即使在这个充满缺陷的二维系统。我们得到的大距离，长时间的标度律的速度波动使用三个不同的动态重整化群计划。这是一个不受控制的单循环计算，正好是二维的，和两个d=（d_{c}-ε）展开到O（ε），通过我们的二维模型的两个不同的解析延拓得到更高的空间维度：一个“硬”延拓，d_{c}=7/3，和一个“软”延拓，d_{c}=5/2。令人惊讶的是，淬火和退火部分的速度相关函数具有相同的各向异性指数和弛豫和传播部分的色散关系具有相同的动力学指数的非线性理论，即使它们是不同的线性化理论。这是由于反常的流体动力学。此外，所有三个重整化方案产生非常相似的普适指数值，因此我们期望我们预测的数值是高度准确的。
We study the moving phase of two-dimensional (2D) incompressible polar active fluids in the presence of both quenched and annealed disorder. We show that long-range polar order persists even in this defect-ridden two-dimensional system. We obtain the large-distance, long-time scaling laws of the velocity fluctuations using three distinct dynamic renormalization group schemes. These are an uncontrolled one-loop calculation in exactly two dimensions, and two d=(d_{c}-ε) expansions to O(ε), obtained by two different analytic continuations of our 2D model to higher spatial dimensions: a "hard" continuation which has d_{c}=7/3, and a "soft" continuation with d_{c}=5/2. Surprisingly, the quenched and annealed parts of the velocity correlation function have the same anisotropy exponent and the relaxational and propagating parts of the dispersion relation have the same dynamic exponent in the nonlinear theory even though they are distinct in the linearized theory. This is due to anomalous hydrodynamics. Furthermore, all three renormalization schemes yield very similar values for the universal exponents, and therefore we expect the numerical values that we predict for them to be highly accurate.