Decoherence from internal degrees of freedom for cluster of mesoparticles : a hierarchy of master equations

A mesoscopic evolution equation for an ensemble of mesoparticles follows after the elimination of internal degrees of freedom. If the system is composed of a hierarchy of scales, the reduction procedure could be worked repeatedly and the characterization of this iterating method is carried out. Namely, a prescription describing a discrete hierarchy of master equations for the density operator is obtained. Decoherence follows from the irreversible coupling of the systems, defined by mesoscopic variables, to internal degrees of freedom. We discuss briefly the existence of systems with the same dynamics laws at different scales. We made an explicit calculation for an ensemble of particles with internal harmonic interaction in an external anharmonic field. New conditions related to the semiclassical limit for mesoscopic systems (Wigner-function) are conjectured.