  State engineering in nonlinear quantum dynamics sometimes may demand driving
the system through a sequence of dynamically unstable intermediate states. This
very general scenario is especially relevant to dilute Bose-Einstein
condensates, for which ambitious control schemes have been based on the
powerful Gross-Pitaevskii mean field theory. Since this theory breaks down on
logarithmically short time scales in the presence of dynamical instabilities,
an interval of instabilities introduces quantum corrections, which may possibly
derail a control scheme. To provide a widely applicable theory for such quantum
corrections, this paper solves a general problem of time-dependent quantum
mechanical dynamical instability, by modelling it as a second-quantized
analogue of a Landau-Zener avoided crossing: a `twisted crossing'.
