  We investigate electron-phonon coupling in many-electron systems using
dynamical mean-field theory in combination with the numerical renormalization
group. This non-perturbative method reveals significant precursor effects to
the gap formation at intermediate coupling strengths. The emergence of a soft
phonon mode and very strong lattice fluctuations can be understood in terms of
Kondo-like physics due to the development of a double-well structure in the
effective potential for the ions.
