  An analytical insight into the symmetry breaking mechanisms underlying the
transition from Josephson to self-trapping regimes in Bose-Einstein condensates
is presented. We obtain expressions for the ground state properties of the
system of a gas of attractive bosons modelized by a two site Bose-Hubbard
hamiltonian with an external bias. Simple formulas are found relating the
appearance of fragmentation in the condensate with the large quantum
fluctuations of the population imbalance occurring in the transition from the
Josephson to the self-trapped regime.
