Velocity and diffusion constant of an active particle in a one dimensional force field

Abstract

We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of period $L$. They involve the "active potential" which allows to define a global bias. Upon varying parameters, such as an external force $F$, the dynamics undergoes transitions from non-ergodic trapped states, to various moving states, some with non analyticities in the $V_L$ versus $F$ curve. A random landscape in the presence of a bias leads, for large $L$, to anomalous diffusion $x\sim t^{\mu }$, $\mu <1$, or to a phase with a finite velocity that we calculate.

7 + 15 pages, 8 figures

References in corpus (7)

• Motility-Induced Phase Separation
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• First-passage time of run-and-tumble particles
• Non-crossing run-and-tumble particles on a line
• Exact Solution of Two Interacting Run-and-Tumble Random Walkers with Finite Tumble Duration
• Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder

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