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arXiv 2102.09944cond-mat.soft
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一维空间摩擦力作用下的主动噪声驱动粒子

Active noise-driven particles under space-dependent friction in one dimension

Davide Breoni, Hartmut Löwen, Ralf Blossey

摘要:

本文研究了一维Langevin方程,该方程描述了一个具有$x$坐标的粒子在空间中的随机运动,该粒子同时受到与空间有关的摩擦系数$γ(x)$、约束势$U(x)$和非平衡态(即,有源)噪声。具体来说,我们考虑摩擦$γ(x)=γ_0 + γ_1 | x |^p$和潜在的$U(x) \propto | x |^n$与指数$p = 1,2$和$n = 0, 1, 2$。我们提供了分析和数值结果的粒子动力学的短时间和平稳的概率密度函数(PDF)的长时间。短时间的行为显示扩散和弹道制度,而固定PDF显示独特的特征,取决于指数值$(p, n)$。PDF在拉普拉斯分布、高斯分布和双峰分布之间插值,由此可以通过调整摩擦强度比$γ_0/γ_1$来实现这些不同行为之间的变化。我们的模型是相关的分子马达在一维轨道上移动,也可以实现受限的自我推进的胶体粒子。

英文摘要:

We study a Langevin equation describing the stochastic motion of a particle in one dimension with coordinate $x$, which is simultaneously exposed to a space-dependent friction coefficient $γ(x)$, a confining potential $U(x)$ and non-equilibrium (i.e., active) noise. Specifically, we consider frictions $γ(x)=γ_0 + γ_1 | x |^p$ and potentials $U(x) \propto | x |^n$ with exponents $p = 1,2$ and $n = 0, 1, 2$. We provide analytical and numerical results for the particle dynamics for short times and the stationary probability density functions (PDFs) for long times. The short-time behaviour displays diffusive and ballistic regimes while the stationary PDFs display unique characteristic features depending on the exponent values $(p, n)$. The PDFs interpolate between Laplacian, Gaussian and bimodal distributions, whereby a change between these different behaviours can be achieved by a tuning of the friction strengths ratio $γ_0/γ_1$. Our model is relevant for molecular motors moving on a one-dimensional track and can also be realized for confined self-propelled colloidal particles.

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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