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 $\gamma \left(x\right)$, a confining potential $U\left(x\right)$ and nonequilibrium (i.e., active) noise. Specifically, we consider frictions $\gamma \left(x\right)={\gamma }_0+{\gamma }_1{\left|x\right|}^p$ and potentials $U\left(x\right)\propto {\left|x\right|}^n$ 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 behavior 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 behaviors can be achieved by a tuning of the friction strengths ratio ${\gamma }_0/{\gamma }_1$. Our model is relevant for molecular motors moving on a one-dimensional track and can also be realized for confined self-propelled colloidal particles.

• Received 19 February 2021
• Accepted 14 April 2021

DOI:https://doi.org/10.1103/PhysRevE.103.052602