Many-body effects in the normal-state polaron system

Dielectric response function of small polarons (SP’s) is studied. The Debye radius is small, which reduces a short-range Coulomb repulsion to the magnitude of the order of the small-polaron (SP) bandwidth. Polaron-polaron attraction is enhanced by screening. A critical temperature of the bipolaron formation is found. The dielectric response becomes dynamic in a very low-frequency region. A multiphonon diagram technique is developed to obtain vibration excitations, that are a mixture of phonons with polaronic plasmons. A microscopic model of the anomalous extra modes, observed in neutron-scattering experiments in ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$, is proposed.