At equilibrium, the structure and response of ordered phases are typically determined by the spontaneous breaking of spatial symmetries. Out of equilibrium, spatial order itself can become a dynamically emergent concept. In this article, we show that spatially anisotropic viscous coefficients and stresses can be designed in a far-from-equilibrium fluid by applying to its constituents a time-modulated drive. If the drive induces a rotation whose rate is slowed down when the constituents point along specific directions, anisotropic structures and mechanical responses arise at long timescales. We demonstrate that the viscous response of anisotropic driven fluids can acquire a tensorial, dissipationless component called anisotropic odd (or Hall) viscosity. Classical fluids with internal torques can display additional components of the odd viscosity neglected in previous studies of quantum Hall fluids that assumed angular momentum conservation. We show that these anisotropic and angular momentum-violating odd-viscosity coefficients can change even the bulk flow of an incompressible fluid by acting as a source of vorticity. In addition, shear distortions in the shape of an inclusion result in torques. We derive how the odd-viscous coefficients depend on the nonlinear, dissipative response of the underlying fluid of rods, i.e., odd viscosity is not simply given by angular momentum density.

中文翻译：

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通过时间调制驱动的各向异性奇粘度

在平衡状态下，有序相的结构和响应通常由空间对称性的自发确定。不平衡，空间秩序本身可能成为动态出现的概念。在本文中，我们表明可以通过将时间调制驱动应用于远非平衡流体，来设计空间各向异性粘性系数和应力。如果驱动器诱导旋转，当成分沿特定方向指向时其速度变慢，则各向异性结构和机械响应会在较长的时间内出现。我们证明了各向异性驱动流体的粘性响应可以获取张量，无耗散的成分，称为各向异性奇（或霍尔）粘度。具有内部扭矩的经典流体可以显示出奇数粘度的其他成分，而在以前的量子霍尔流体研究中，这些粘度被假定为角动量守恒。我们表明，这些各向异性和违反角动量的奇粘度系数甚至可以通过充当涡旋源来改变不可压缩流体的整体流量。另外，夹杂物形状的剪切变形导致扭矩。我们得出奇数粘滞系数如何取决于杆的基础流体的非线性耗散响应，即，奇数粘度不是简单地由角动量密度给出。我们表明，这些各向异性和违反角动量的奇粘度系数甚至可以通过充当涡旋源来改变不可压缩流体的整体流量。另外，夹杂物形状的剪切变形导致扭矩。我们得出奇数粘滞系数如何取决于杆的基础流体的非线性耗散响应，即，奇数粘度不是简单地由角动量密度给出。我们表明，这些各向异性和违反角动量的奇粘度系数甚至可以通过充当涡旋源来改变不可压缩流体的整体流量。另外，夹杂物形状的剪切变形导致扭矩。我们得出奇数粘滞系数如何取决于杆的基础流体的非线性耗散响应，即，奇数粘度不是简单地由角动量密度给出。