## Many-polaron theory for superconductivity and charge-density waves in a strongly coupled electron-phonon system with quasi-two-dimensionality: An interpolation between the adiabatic limit and the inverse-adiabatic limit

The phase diagram of a two-dimensional N-site N-electron system (N>>1) with site-diagonal electron-phonon (e-ph) coupling is studied in the context of polaron theory, so as to clarify the competition between the superconducting (SC) state and the charge-density wave (CDW) state. The Fermi surface of noninteracting electrons is assumed to be a complete circle with no nesting-type instability in the case of weak e-ph coupling, so as to focus on such a strong coupling that even the standard ''strong-coupling theory'' for superconductivity breaks down. Phonon clouds moving with electrons as well as a frozen phonon are taken into account by amore »