Electron gas with polaronic effects: beyond the mean-field theory

The occurrence of polaronic behaviour in real solids is often accompanied by strong exchange and correlation effects in the electron gas besides being strongly entangled to the phononic degrees of freedom. Such effects can be relevant for the instability towards Wigner crystallization or charge density waves, or yet for the polaron role in high-T(C) superconductors and in manganites. The inclusion of exchange and correlation in the coupled electron-phonon system is thus highly desirable. In this work, we exploit the density functional theory and its time-dependent extension to construct an appropriate effective potential useful for studying the properties of interacting polarons. The validity and the possible developments of this approach are discussed, and future applications are proposed.