  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.
