  We study the time evolution of one-dimensional systems of fermions with
long-range interactions in the presence of strong disorder. Exact
diagonalization of small systems supports many-body localization for weak
Coulomb and dipolar interactions at high energy. The dephasing time of far
apart degrees of freedom is analyzed. The result indicates that von Neumann
entropy of one halve of the system evolves as a power law on time for a
disentangled initial state. The numerical simulations performed in the Coulomb
and dipolar cases are consistent with this prediction.
