Context : The migration of magnetic bright point-like features ( MBP ) in the lower solar atmosphere reflects the dispersal of magnetic flux as well as the horizontal flows of the atmospheric layer they are embedded in .

Aims : We analyse trajectories of the proper motion of intrinsically magnetic , isolated internetwork Ca ii H MBPs ( mean lifetime 461 \pm 9 ~ { } \mathrm { sec } ) to obtain their diffusivity behaviour .

Methods : We use seeing-free high spatial and temporal resolution image sequences of quiet-Sun , disc-centre observations obtained in the Ca ii H 3968 ~ { } \mathrm { \AA } passband of the Sunrise Filter Imager ( SuFI ) onboard the Sunrise balloon-borne solar observatory .
Small MBPs in the internetwork are automatically tracked .
The trajectory of each MBP is then calculated and described by a diffusion index ( \gamma ) and a diffusion coefficient ( D ) .
We also explore the distribution of the diffusion indices with the help of a Monte Carlo simulation .

Results : We find \gamma = 1.69 \pm 0.08 and D = 257 \pm 32 ~ { } \mathrm { km } ^ { 2 } \mathrm { s } ^ { -1 } averaged over all MBPs .
Trajectories of most MBPs are classified as super-diffusive , i.e . \gamma > 1 , with the determined \gamma being the largest obtained so far to our knowledge .
A direct correlation between D and timescale ( \tau ) determined from trajectories of all MBPs is also obtained .
We discuss a simple scenario to explain the diffusivity of the observed , relatively short-lived MBPs while they migrate within a small area in a supergranule ( i.e .
an internetwork area ) .
We show that the scatter in the \gamma values obtained for individual MBPs is due to their limited lifetimes .

Conclusions : The super-diffusive MBPs can be described as random walkers ( due to granular evolution and intergranular turbulence ) superposed on a large systematic ( background ) velocity , caused by granular , mesogranular , and supergranular flows .