  We study the quantum dynamics of strongly interacting few-boson mixtures in
one-dimensional traps. If one species is strongly localized compared to the
other (e.g., much heavier), it can serve as an effective potential barrier for
that mobile component. Near the limit of infinite localization, we map this to
a system of identical bosons in a double well. For realistic localization, the
backaction of the light species on the "barrier" atoms is explained--to lowest
order--in terms of an induced attraction between these. Even in equilibrium,
this may outweigh the bare intra-species interaction, leading to unexpected
correlated states. Remarkably, the backaction drastically affects the
inter-species dynamics, such as the tunneling of an attractively bound pair of
fermionized atoms.
