Anharmonic Vibrations in Ordered and Disordered One- And Two-Dimensional Systems

We present extensive results of computer simulations on vibrations in one- and two-dimensional lattices with quartic anharmonicity. The existence of localized mode in ordered lattice is confirmed but the long term stability is questionable. Rather our results indicate an ergodic behavior at large times when several modes are present. Concerning disordered systems we have found that anharmonicity leads to a surprising new phenomenon of anomalous diffusion and thus to the possibility of anharmonically induced transport.