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 $\gamma=2/3$ 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