  Recent experiments with a rotating probe immersed in weakly fluidized
granular materials show a complex behavior on a wide range of timescales.
Viscous-like relaxation at high frequency is accom- panied by an almost
harmonic dynamical trapping at intermediate times, with possibly anomalous long
time behavior in the form of super-diffusion. Inspired by the Itinerant
Oscillator model for dif- fusion in molecular liquids, and other models with
coupled thermostats acting at different timescales, here we discuss a new model
able to account for fast viscous relaxation, dynamical trapping and
super-diffusion at long times. The main difference with respect to liquids, is
a non-negligible cage inertia for the surrounding (granular) fluid, which
allows it to sustain a slow but persistent mo- tion for long times. The
computed velocity power density spectra and mean-squared displacement
qualitatively reproduce the experimental findings. We also discuss the linear
response to external perturbations and the tail of the distribution of
persistency time, which is associated with superdif- fusion, and whose cut-off
time is determined by cage inertia.
