  We show that the presence of a harmonic trap may in itself lead to many-body
localization for cold atoms confined in that trap in a quasi-one-dimensional
geometry. Specifically, the coexistence of delocalized phase in the center of
the trap with localized region closer to the edges is predicted with the
borderline dependent on the curvature of the trap. The phenomenon, similar in
its origin to Stark localization, should be directly observed with cold atomic
species. We discuss both the spinless and the spinful fermions, for the latter
we address Stark localization at the same time as it has not been analyzed up
till now.
