  We obtain dynamical lower bounds for some self-adjoint operators with pure
point spectrum in terms of the spacing properties of their eigenvalues. In
particular, it is shown that for systems with thick point spectrum, typically
in Baire's sense, the dynamics of each initial condition (with respect to some
orthonormal bases of the space) presents a quasiballistic behaviour. We present
explicit applications to some Schr\"odinger operators.
