MACROSCOPIC LIMITING DYNAMICS OF A CLASS OF INHOMOGENEOUS MEAN FIELD QUANTUM-SYSTEMS

We study a class of Hamiltonian systems with inhomogeneous (i.e. site- dependent) mean field interactions. We define some notions of mean fie ld limit for nets of states converging to a macroscopic limit state. W e prove that the existence of such limits is preserved under the time evolution. This leads to a time evolution for the macroscopic limit st ates, i.e. to a closed set of equations for some macroscopic fields. W e establish the basic properties of these equations, and their relatio n to the equilibrium statistical mechanics of the same systems. We dis cuss in detail the connection of our work to the problem of local equi librium states, which motivated it.