Effects of random localizing events on matter waves: formalism and   examples
  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. 
Julio Gea-Banacloche