  We introduce the notion of transmission time to study the dynamics of
disordered quantum spin chains and prove results relating its behavior to
many-body localization properties. We also study two versions of the so-called
Local Integrals of Motion (LIOM) representation of spin chain Hamiltonians and
their relation to dynamical many-body localization. We prove that
uniform-in-time dynamical localization expressed by a zero-velocity
Lieb-Robinson bound implies the existence of a LIOM representation of the
dynamics as well as a weak converse of this statement. We also prove that for a
class of spin chains satisfying a form of exponential dynamical localization,
sparse perturbations result in a dynamics in which transmission times diverge
at least as a power law of distance, with a power for which we provide lower
bound that diverges with increasing sparseness of the perturbation.
