  A formalism is introduced to describe a number of physical processes that may
break down the coherence of a matter wave over a characteristic length scale l.
In a second-quantized description, an appropriate master equation for a set of
bosonic "modes" (such as atoms in a lattice, in a tight-binding approximation)
is derived. Two kinds of "localizing processes" are discussed in some detail
and shown to lead to master equations of this general form: spontaneous
emission (more precisely, light scattering), and modulation by external random
potentials. Some of the dynamical consequences of these processes are
considered: in particular, it is shown that they generically lead to a damping
of the motion of the matter-wave currents, and may also cause a "flattening" of
the density distribution of a trapped condensate at rest.
