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A vertically shaken granular medium hosts a blade rotating around a
fixed vertical axis, which acts as a mesorheological probe. At
high densities, independently from the shaking intensity, the blade's
dynamics show strong caging effects, marked by transient
sub-diffusion and a maximum in the velocity power density spectrum
(vpds), at a resonant frequency $\sim 10$ Hz. Interpreting the data through a diffusing harmonic cage model allows us to retrieve the elastic
constant of the granular medium and its collective diffusion
coefficient. For high frequencies in the vpds, a $1/f$-tail
reveals non-trivial correlations in the intra-cage micro-dynamics. At
very long times (larger than $10$ s), a super-diffusive behavior emerges, ballistic in the most extreme cases. Consistently, the distribution of slow velocity inversion times $\tau$ displays a power-law decay, likely due to persistent collective fluctuations of the host medium.
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