Driven particle in a cloud of mobile impurities

The dynamics of a test particle interacting with diffusing impurities in one dimension is investigated analytically and numerically. In the absence of an applied external force, the dynamics of the particle can be characterized by a distribution of monotonic excursions $\Delta x$, which scales as a power law with an exponent $\tau_{\Delta x} = 4/3$. When the particle is driven at a slow constant velocity, there is again a power law distribution for the monotonic changes of the force $\Delta F$, which is characterized by a similar exponent $\tau_{\Delta F}=4/3$. These results can be understood from the theory of random walks.