Self-Quenched Dynamics

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 $\gamma =2\mathrm{/}3$ 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.