Self-quenched dynamics

We introduce a model fur the slow relaxation of an energy landscape caused by its local interaction with a random walker whose motion is dictated by t he landscape itself. By choosing relevant measure of time and potential thi s self-quenched dynamics can be mapped on to the "True" Self-Avoiding Walk model. This correspondance reveals that the average distance of the walker at time t from its starting point is R(t) similar to log(t)(0), where gamma = 2/3 for one dimension and 1/2 for all higher dimensions. Furthermore, th e evolution of thc landscape is similar to that in growth models with exter nal dynamics.