Chaotic diffusion and 1/f-noise of particles in two-dimensional solids

We investigate the classical nonlinear dynamics of a particle moving conservatively in a two-dimensional periodic potential. The particle exhibits diffusive motion in the absence of random forces. In a broad range of energies above the potential barrier, the diffusion process is anomalously accelerated and associated with 1/f-noise in the power spectrum of velocity fluctuations. The analysis of Poincaré surfaces of section and the distribution of free paths indicate that the phenomenon is caused by a trapping of orbits in a self-similar hierarchy of nested cantori. We describe a statistical theory for this mechanism in terms of a renewal process and a random walk on a hierarchical lattice.Work supported by Deutsche Forschungsgemeinschaft