  We establish uniform bounds for the solutions $e^{it\Delta}u$ of the
Schr\"{o}dinger equation on arithmetic flat tori, generalising earlier results
by J. Bourgain. We also study the regularity properties of weak-* limits of
sequences of densities of the form $|e^{it\Delta}u_{n}|^{2}$ corresponding to
highly oscillating sequences of initial data $(u_{n})$. We obtain improved
regularity properties of those limits using previous results by N. Anantharaman
and F. Maci\`a on the structure of semiclassical measures for solutions to the
Schr\"{o}dinger equation on the torus.
