The dynamic properties of the quiet Sun photosphere can be investigated by analyzing the pair dispersion of small-scale magnetic fields ( i.e. , magnetic elements ) .
By using 25 hr-long Hinode magnetograms at high spatial resolution ( 0 " .3 ) , we tracked 68 , 490 magnetic element pairs within a supergranular cell near the disk center .
The computed pair separation spectrum , calculated on the whole set of particle pairs independently of their initial separation , points out what is known as a super-diffusive regime with spectral index \gamma = 1.55 \pm 0.05 , in agreement with the most recent literature , but extended to unprecedented spatial and temporal scales ( from granular to supergranular ) .
Furthermore , for the first time , we investigated here the spectrum of the mean square displacement of pairs of magnetic elements , depending on their initial separation r _ { 0 } .
We found that there is a typical initial distance above ( below ) which the pair separation is faster ( slower ) than the average .
A possible physical interpretation of such a typical spatial scale is also provided .