We address ourselves to a class of systems composed of two coupled subsystems
without any intra-subsystem interaction: itinerant Fermions and localized
Bosons on a lattice. Switching on an interaction between the two subsystems
leads to feedback effects which result in a rich dynamical structure in both of
them. Such feedback features are studied on the basis of the flow equation
technique - an infinite series of infinitesimal unitary transformations - which
leads to a gradual elimination of the inter-subsystem interaction. As a result
the two subsystems get decoupled but their renormalized kinetic energies become
mutually dependent on each other. Choosing for the inter - subsystem
interaction a charge exchange term (the Boson-Fermion model) the initially
localized Bosons acquire itinerancy through their dependence on the
renormalized Fermion dispersion. This latter evolves from a free particle
dispersion into one showing a pseudogap structure near the chemical potential.
Upon lowering the temperature both subsystems simultaneously enter a
macroscopic coherent quantum state. The Bosons become superfluid, exhibiting a
soundwave like dispersion while the Fermions develop a true gap in their
dispersion. The essential physical features described by this technique are
already contained in the renormalization of the kinetic terms in the respective
Hamiltonians of the two subsystems. The extra interaction terms resulting in
the process of iteration only strengthen this physics. We compare the results
with previous calculations based on selfconsistent perturbative approaches.Comment: 14 pages, 16 figures, accepted for publication in Phys. Rev.