Transport in Nanostructures - a Paradigm for Complex Nonlinear Dynamics and Pattern Formation

Shmuel Fishman,

Israel Institute of Technology

For idealized classical chaotic systems (hyperbolic systems), distributions of phase space trajectories relax to an equilibrium density. This relaxation is similar to the one that takes place for large systems, that are traditionally studied in statistical physics. For realistic systems, where in some parts of phase space the motion is regular and in some parts it is chaotic, there is no rigorous theory for relaxation. An approximate theory, relevant for such systems will be presented. It will be demonstrated for the kicked rotor (standard map) that is extensively studied in the field of chaos.