Stochastic fluid dynamics governs the long time tails of hydrodynamic correlation functions, and the critical slowing down of relaxation phenomena in the vicinity of a critical point in the phase diagram. In this work we study the role of multiplicative noise in stochastic fluid dynamics. Multiplicative noise arises from the dependence of transport coefficients, such as the diffusion constants for charge and momentum, on fluctuating hydrodynamic variables. We study long time tails and relaxation in the diffusion of a conserved density (model B), and a conserved density coupled to the transverse momentum density (model H). Careful attention is paid to fluctuation-dissipation relations. We observe that multiplicative noise contributes at the same order as non-linear interactions in model B, but is a higher order correction to the relaxation of a scalar density and the tail of the stress tensor correlation function in model H.

中文翻译：

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乘法噪声和守恒密度的扩散

随机流体动力学控制着流体动力学相关函数的长时间尾部，以及相图中临界点附近松弛现象的临界减慢。在这项工作中，我们研究了乘法噪声在随机流体动力学中的作用。乘性噪声源于传输系数（例如电荷和动量的扩散常数）对波动的流体动力学变量的依赖性。我们研究了守恒密度（模型 B）和与横向动量密度耦合的守恒密度（模型 H）的扩散中的长时间拖尾和弛豫。仔细注意波动-耗散关系。我们观察到乘法噪声的贡献与模型 B 中的非线性相互作用相同，