Polarons in quasi-one-dimensional systems

We discuss the nature of polaron excitations in two models of current interest in the study of quasi-one-dimensional materials: the coupled electron-phonon and molecular-crystal models. Using for definiteness parameters appropriate to trans-${\left(\mathrm{CH}\right)}_x$, we show that, although qualitatively very similar, the two polarons differ quantitatively in many respects. We then consider the very weakly bound polaron limit and show that here the two polarons become identical. We indicate that this limit, although not applicable to trans-${\left(\mathrm{CH}\right)}_x$, may be relevant to other interesting quasi-one-dimensional materials.