Polaron conductivity in the narrow-band Hubbard model

We consider a Hubbard model in which electrons are locally coupled to the lattice and form polarons. The frequency-dependent polaron conductivity ${\mathrm{\sigma }}_{\mathrm{pot}}$(ω) is calculated in the narrow-band limit as a function of electron density. There are two contributions: a band term that arises from coherent motion of dressed electrons and a hopping term that describes the incoherent process by which electrons ‘‘shake off’’ their polaron distortion. The possible relevance of these results to the structure in σ(ω) observed in high-${\mathit{T}}_{\mathit{c}}$ superconductors is briefly discussed.