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arXiv 1402.4598cond-mat.stat-mechcond-mat.softphysics.comp-ph
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摩擦力空间变化系统的涨落耗散关系

Fluctuation-dissipation relation for systems with spatially varying friction

Oded Farago, Niels Grønbech-Jensen

备注：
11 pages, 6 figures. Minor revisions to previous version. Accepted for publication in J. Stat. Phys
发表信息：
J. Stat. Phys. 156, 1093 (2014)
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摘要：

当一个粒子在具有空间相关摩擦系数$α(r)$的介质中扩散时，即使在没有任何实际物理力$f$的情况下，在恒定温度$T$下，它也会向系统的低摩擦端漂移。这种现象，这是以前研究的背景下，非惯性布朗动力学，被称为“假漂移”，虽然漂移是真实的，源于惯性效应发生在短时间尺度。在这里，我们研究的非均匀介质中的惯性朗之万方程的框架内的粒子的扩散。我们证明了表征非均匀$α(r)$动力学的量不是粒子$Δr=r-r^0$的位移（其中$r^0$是初始位置），而是$ΔA(r)=A(r)-A(r^0)$，其中$A(r)$是$α(r)$的原函数。我们推导出表达式的平均值和方差的$ΔA$的$f$，$T$，和持续时间的动态$Δt$。对于恒定的摩擦系数$α(r)=α$，这些表达式简化为众所周知的力-漂移和波动-耗散关系的形式。我们介绍了一个非常准确的方法，朗之万动力学模拟系统的空间变化$α(r)$，并使用该方法来验证新推导的表达式。

英文摘要：

When a particle diffuses in a medium with spatially dependent friction coefficient $α(r)$ at constant temperature $T$, it drifts toward the low friction end of the system even in the absence of any real physical force $f$. This phenomenon, which has been previously studied in the context of non-inertial Brownian dynamics, is termed "spurious drift", although the drift is real and stems from an inertial effect taking place at the short temporal scales. Here, we study the diffusion of particles in inhomogeneous media within the framework of the inertial Langevin equation. We demonstrate that the quantity which characterizes the dynamics with non-uniform $α(r)$ is not the displacement of the particle $Δr=r-r^0$ (where $r^0$ is the initial position), but rather $ΔA(r)=A(r)-A(r^0)$, where $A(r)$ is the primitive function of $α(r)$. We derive expressions relating the mean and variance of $ΔA$ to $f$, $T$, and the duration of the dynamics $Δt$. For a constant friction coefficient $α(r)=α$, these expressions reduce to the well known forms of the force-drift and fluctuation-dissipation relations. We introduce a very accurate method for Langevin dynamics simulations in systems with spatially varying $α(r)$, and use the method to validate the newly derived expressions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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