Hydrodynamics is a universal effective theory that describes the thermalization of chaotic many-body systems, and depends only on the symmetries of the underlying theory. Although the Navier–Stokes equations can describe classical liquids and gases, quantum fluids of ultracold atoms or quark–gluon plasma, they cannot yet describe the phases of matter where particle motion is kinematically constrained. Here we present the nonlinear fluctuating hydrodynamics of models with simultaneous charge/mass, dipole/centre of mass and momentum conservation. This hydrodynamic effective theory is unstable below four spatial dimensions: dipole-conserving fluids at rest are unstable to fluctuations, which drive the system to a dynamical universality class with qualitatively distinct features from conventional fluids. In one spatial dimension, our construction is reminiscent of the well-established renormalization group flow of the stochastic Navier–Stokes equations; however, the fixed point we find possesses subdiffusive scaling rather than the superdiffusive scaling of the Kardar–Parisi–Zhang universality class. We numerically simulate many-body classical dynamics in one- and two-dimensional models with dipole and momentum conservation, and find evidence for the predicted breakdown of hydrodynamics. Our theory provides a controlled example of how kinematic constraints lead to a rich landscape of dynamical universality classes in high-dimensional models.

流体动力学是描述混沌多体系统热化的普遍有效理论，仅依赖于基础理论的对称性。尽管 Navier-Stokes 方程可以描述经典的液体和气体、超冷原子的量子流体或夸克-胶子等离子体，但它们还不能描述粒子运动受到运动学约束的物质相。在这里，我们介绍了同时具有电荷/质量、偶极子/质量中心和动量守恒的模型的非线性波动流体动力学。这种流体动力学有效理论在四个空间维度以下是不稳定的：静止的偶极守恒流体对波动不稳定，这将系统推向具有与常规流体在性质上不同的特征的动力学普遍性类别。在一个空间维度上，我们的构造让人想起随机 Navier-Stokes 方程的成熟的重整化群流；然而，我们发现的固定点具有亚扩散尺度，而不是 Kardar-Parisi-Zhang 普适性类的超扩散尺度。我们在具有偶极子和动量守恒的一维和二维模型中对多体经典动力学进行数值模拟，并找到预测的流体动力学崩溃的证据。我们的理论提供了一个受控示例，说明运动学约束如何导致高维模型中动态普遍性类的丰富景观。我们发现的不动点具有亚扩散尺度，而不是 Kardar-Parisi-Zhang 普遍性类的超扩散尺度。我们在具有偶极子和动量守恒的一维和二维模型中对多体经典动力学进行数值模拟，并找到预测的流体动力学崩溃的证据。我们的理论提供了一个受控示例，说明运动学约束如何导致高维模型中动态普遍性类的丰富景观。我们发现的不动点具有亚扩散尺度，而不是 Kardar-Parisi-Zhang 普遍性类的超扩散尺度。我们在具有偶极子和动量守恒的一维和二维模型中对多体经典动力学进行数值模拟，并找到预测的流体动力学崩溃的证据。我们的理论提供了一个受控示例，说明运动学约束如何导致高维模型中动态普遍性类的丰富景观。