边界诱导的漂移与受限随机系统中的负迁移
Boundary-Induced Drift and Negative Mobility in Constrained Stochastic Systems
AI总结：
研究受限随机动力学中边界几何与各向异性扩散张量的组合如何产生定向运动，并通过一维双粒子系统展示局部边界诱导漂移如何导致宏观传输，包括恒定力下的绝对负迁移。
摘要：
我们研究了受硬反射边界约束的过阻尼随机动力学，并展示边界几何与各向异性扩散张量的组合通常会生成定向运动。在个体轨迹层面，无净流条件强制在边界处产生斜向反射，从而产生平行于表面的系统漂移。所得到的局部速度具有一般形式 $v_B(\mathbf{x})=\mathbf{t}(\mathbf{x})^{\!\top}\mathbf{D}\,\mathbf{n}(\mathbf{x})$，由扩散张量 $\mathbf{D}$ 和局部边界几何编码在法向 $\mathbf{n}$ 和切向 $\mathbf{t}$ 中决定。尽管这种边界诱导的漂移是局部的，但根据边界接触的统计特性，它可以积累为宏观响应。我们通过一个由两个扩散系数不等的粒子组成的最小一维二元系统，展示了这种局部边界诱导漂移如何导致宏观传输。重复碰撞在配置空间中起反射作用，并导致持续的质心运动，包括在恒定力下的绝对负迁移 regime。
英文摘要：
We study overdamped stochastic dynamics confined by hard reflecting boundaries and show that the combination of boundary geometry and an anisotropic diffusion tensor generically generates directed motion. At the level of individual trajectories, the no-flux condition enforces an oblique reflection at the boundary, which produces a systematic drift parallel to the surface. The resulting local velocity takes the general form $v_B(\mathbf{x})=\mathbf{t}(\mathbf{x})^{\!\top}\mathbf{D}\,\mathbf{n}(\mathbf{x})$, determined by the diffusion tensor $\mathbf{D}$ and the local boundary geometry encoded in the normal $\mathbf{n}$ and tangent $\mathbf{t}$. While this boundary-induced drift is local, it can accumulate into a macroscopic response, depending on the statistics of boundary encounters. We illustrate how this local boundary-induced drift gives rise to macroscopic transport using a minimal one-dimensional dimer composed of two particles with unequal diffusion coefficients. The repeated collisions act as reflections in configuration space and lead to sustained center-of-mass motion, including regimes of absolute negative mobility under constant forcing.
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