标题： 自由液态扩散中长程非平衡关联的出现 显示英文标题

标题： Emergence of long-range non-equilibrium correlations in free liquid diffusion

摘要： 实验上已充分确立，在溶质在溶剂中的自由扩散中会出现浓度涨落的非平衡长程关联，但这种关联是如何动态建立的仍不清楚。 我们针对Donev、Fai与Vanden-Eijnden（DFV）的模型来解决这个问题，该模型来源于二元混合物的Landau-Lifschitz涨落流体力学方程的高Schmidt数极限。 我们考虑无限空间域中平均浓度场的初始平面界面，以理想化先前的实验。 利用来自湍流理论的方法，我们既通过分析又通过数值方法证明，在长时间后会出现一个准稳态阶段，其中浓度关联的时间衰减具有自相似性。 除了预期的“巨大浓度涨落”与相关性$\propto r$对$r\lesssim L(t)=(Dt)^{1/2},$以及扩散率$D,$，对于$r\gtrsim L(t).$出现了一个新的具有空间衰减$\propto 1/r$的区域。准稳态区域来源于瞬态增长的初始阶段$\propto t,$，证实了DFV对$r\gtrsim L(t)$的预测，并发现了对$r\lesssim L(t).$的类似结果。我们的结果为非平衡长程关联的出现提供了新的见解，并提供了可能通过实验进行研究的新预测。 显示英文摘要

摘要： It is experimentally well-established that non-equilibrium long-range correlations of concentration fluctuations appear in free diffusion of a solute in a solvent, but it remains unknown how such correlations are established dynamically. We address this problem in a model of Donev, Fai \& Vanden-Eijnden (DFV), obtained from the high-Schmidt limit of the Landau-Lifschitz fluctuating hydrodynamic equations for a binary mixture. We consider an initial planar interface of the mean concentration field in an infinite space domain, idealizing prior experiments. Using methods borrowed from turbulence theory, we show both analytically and numerically that a quasi-steady regime with self-similar time decay of concentration correlations appears at long time. In addition to the expected ``giant concentration fluctuations'' with correlations $\propto r$ for $r\lesssim L(t)=(Dt)^{1/2},$ with diffusivity $D,$ a new regime with spatial decay $\propto 1/r$ appears for $r\gtrsim L(t).$ The quasi-steady regime arises from an initial stage of transient growth $\propto t,$ confirming the prediction of DFV for $r\gtrsim L(t)$ and discovering an analogous result for $r\lesssim L(t).$ Our results give new insight into the emergence of non-equilibrium long-range correlations and provide novel predictions that may be investigated experimentally.