  The stability of a low temperature Bose-Einstein condensate with attractive
interactions in one and three dimensional double-well potentials is discussed.
In particular, the tunnelling dynamics of a condensate under the influence of a
time-dependent potential gradient is investigated. The condensate is shown to
collapse at a critical potential gradient which corresponds to a critical
number of atoms in one of the two wells. The sensitivity of this tunnelling
induced collapse could provide a useful tool in the study of condensates with
attractive interactions.
