Uphill Drift in the Absence of Current in Single-File Diffusion,Physical Review Letters

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Uphill Drift in the Absence of Current in Single-File Diffusion
Physical Review Letters ( IF 8.1 ) Pub Date : 2024-09-03 , DOI: 10.1103/physrevlett.133.107101
Benjamin Sorkin ₁ , David S. Dean _{2,

2}

Affiliation

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 uphill drift toward the region of highest potential. This drift has the late time behavior

⟨ Y (t) ⟩ = 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.

中文翻译：

单列扩散中无电流情况下的上坡漂移

单列扩散是布朗胶体颗粒在狭窄的一维通道中传输的范例模型，例如在某些多孔介质中发现的通道，其中颗粒不能相互交叉。我们考虑一个系统，其中原点的右侧和左侧存在不同的外部均匀电势。例如，当两个在原点相遇的通道具有不同的半径时，就会出现这种情况。在平衡状态下，颗粒的化学势相等，因此具有较高电势的区域的密度较低，并且根据定义，系统中不存在净电流。值得注意的是，单列示踪粒子最初位于原点，位置表示为