Simple System with Quasiperiodic Dynamics: a Spin in a Magnetic Field

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Abstract
A very simple system with quasiperiodic dynamics is introduced, consisting of a single spin, with spin ½, in a pulsed magnetic field. The pulses are of two types, and the two types alternate in a quasiperiodic way. By adapting renormalization-group and dynamical-systems techniques first introduced in the study of one-dimensional quasiperiodic structures, I characterize the long-time behavior as a function of the experimental parameters. Within different well-defined regions of parameters space, the time correlations decay (a) more slowly than a power law, (b) as a power law, or (c) faster than a power law, and probably exponentially.