  We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein
condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian
of Bose-Hubbard type: The corresponding mean-field system described by a
discrete nonlinear Schr\"odinger equation can show a dynamical (or modulation)
instability due to chaotic dynamics and equipartition over the quasimomentum
modes. It is shown, that these phenomena are related to a depletion of the
Floquet-Bogoliubov states and a decoherence of the condensate in the
many-particle description. Three different types of dynamics are distinguished:
(i) decaying oscillations in the region of dynamical instability, and (ii)
persisting Bloch oscillations or (iii) periodic decay and revivals in the
region of stability.
