Dynamics of a particle in an external potential interacting with a dissipative environment

The study of the recently introduced model of a particle in a periodic potential interacting with an external environment has been pursued, and two main new results are reported: (i) The Hamiltonian is exactly soluble for a particular value of the friction coefficient, {η}={}{π}/a², a being the lattice constant. Earlier results based on the scaling laws obeyed by the model are confirmed. (ii) The influence of imperfections in the potential on the phase diagram of the system is analyzed. It is shown that near impurities, or at a surface, a new localized phase appears.