Detecting pairing and polarization crossovers in systems with retarded interactions

In a system where a boson (e.g., a phonon) of finite frequency omega(0) is coupled to electrons, two phenomena occur as the coupling is increased: local electron pairing via multiple boson exchanges and polarization of the boson field. Within a path integral formalism in a dynamical mean-field approach, we introduce two distribution functions which allow us to pinpoint the two effects. When coo is smaller than the bandwidth D, pairing and polarization occur for fairly similar couplings for all considered temperatures. When omega(0) > D, the two phenomena tend to coincide only for T >> omega(0), but are no longer tied for low temperatures so that a state of local pairs without finite polarization is stabilized. (c) 2007 Elsevier B.V. All rights reserved.