COMPLEXITY IN QUANTUM-SYSTEMS

We discuss the behavior of a quantum 1/2 spin coupled to a time dependent magnetic field, which can be quasiperiodic or random. For a quasiperiodic field, the time evolution of the system on a coarse grained space has autocorrelation, which does not decay, and positive topological entropy. The information complexity diverges as a stretched exponential, although the Shannon entropy is sero, and there is no divergence of nearby orbits. A simple random process is introduced in order to reproduce the main qualitative features of the observed weakly complex behavior.