  We study quantum effects in the dynamics of a Bose-Einstein condensate loaded
onto the edge of a Brillouin zone of a one-dimensional periodic potential
created by an optical lattice. We show that quantum fluctuations trigger the
dynamical instability of the Bloch states of the condensate and can lead to the
generation of arrays of matter-wave gap solitons. Our approach also allows us
to study the instability-induced anomalous heating of the condensate at the
edge of the Brillouin zone and growth of the uncondensed atomic fraction. We
demonstrate that there are regimes in which the heating effects do not suppress
the formation of the localised states. We show that a phase imprinting
technique can ensure the formation of gap soliton trains after short evolution
times and at fixed positions.
