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

Abstract

Abstract We consider a run-and-tumble particle with two velocity states , 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 vs . F curve. A random landscape in the presence of a bias leads, for large L , to anomalous diffusion , , or to a phase with a finite velocity that we calculate.

Topics & Concepts