  We introduce a model for the slow relaxation of an energy landscape caused by
its local interaction with a random walker whose motion is dictated by the
landscape itself. By choosing relevant measures of time and potential this
self-quenched dynamics can be mapped on to the ``True'' Self-Avoiding Walk
model. This correspondence reveals that the average distance of the walker at
time $t$ from its starting point is $R(t)\sim\log(t)^\gamma$, where
$\gamma=2/3$ for one dimension and 1/2 for all higher dimensions. Furthermore,
the evolution of the landscape is similar to that in growth models with
extremal dynamics.
