  We study energy and particle transport for one-dimensional strongly
interacting bosons through a single channel connecting two atomic reservoirs.
We show the emergence of particle- and energy- current separation, leading to
the violation of the Wiedemann-Franz law. As a consequence, we predict
different time scales for the equilibration of temperature and particle
imbalances between the reservoirs. Going beyond the linear spectrum
approximation, we show the emergence of ther- moelectric effects, which could
be controlled by either tuning interactions or the temperature. Our results
describe in a unified picture fermions in condensed matter devices and bosons
in ultracold atom setups. We conclude discussing the effects of a controllable
disorder.
