  The interplay of noise and quantum coherence in transport gives rise to rich
dynamics relevant for a variety of systems. In this work, we put forward a
proposal for an experiment testing noise-induced transport in the vibrational
modes of a chain of trapped ions. We focus on the case of transverse modes,
considering multiple-isotope chains and an "angle trap", where the transverse
trapping varies along the chain. This variation induces localization of the
motional modes and therefore suppresses transport. By suitably choosing the
action of laser fields that couple to the internal and external degrees of
freedom of the ions, we show how to implement effective local dephasing on the
modes, broadening the vibrational resonances. This leads to an overlap of the
local mode frequencies, giving rise to a pronounced increase in the transport
of excitations along the chain. We propose an implementation and measurement
scheme which require neither ground-state cooling nor low heating rates, and we
illustrate our results with a simulation of the dynamics for a chain of three
ions.
