单列扩散中无电流情况下的上坡漂移
Uphill drift in the absence of current in single-file diffusion
AI总结：
本文研究单列扩散中无净电流时示踪粒子的上坡漂移现象，证明其平均位移随时间以$t^{1/4}$增长，并通过解析计算和数值模拟验证了该结果。
摘要：
单列扩散是描述布朗胶体粒子在狭窄一维通道中输运的典型模型，例如在某些多孔介质中，粒子无法相互穿越。我们考虑一个系统，其中原点左右两侧存在不同的外部均匀势。例如，当两个在原点处交汇的通道具有不同半径时，就会出现这种情况。在平衡态下，粒子的化学势相等，因此在势较高的区域密度较低，并且根据定义，系统中不存在净电流。值得注意的是，一个初始位于原点的单列示踪粒子，其位置记为$Y(t)$，表现出朝最高势区域的平均上坡漂移。这种漂移具有晚期行为$\langle Y(t)\rangle= C t^{1/4}$，其中前置因子$C$取决于初始粒子排列。这一令人惊讶的结果通过一种简单且物理意义明确的方法计算$Y(t)$的前两阶矩而得到解析证明，同时也通过大量数值模拟得到了验证。
英文摘要：
Single-file diffusion is a paradigmatic model for the transport of Brownian colloidal particles in narrow one-dimensional channels, such as those found in certain porous media, where the particles cannot cross each other. We consider a system where a different external uniform potential is present to the right and left of an origin. For example, this is the case when two channels meeting at the origin have different radii. In equilibrium, the chemical potential of the particles are equal, the density is thus lower in the region with the higher potential, and by definition there is no net current in the system. Remarkably, a single-file tracer particle initially located at the origin, with position denoted by $Y(t)$, exhibits an average up-hill drift toward the region of highest potential. This drift has the late time behavior $\langle Y(t)\rangle= C t^{1/4}$, where the prefactor $C$ depends on the initial particle arrangement. This surprising result is shown analytically by computing the first two moments of $Y(t)$ through a simple and physically-illuminating method, and also via extensive numerical simulations.
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