To the relation between energies of molecular soliton and extended states in chains

Abstract

A standard statement is that in the interacting electron (exciton) — phonon systems in molecular chains and on the level of the standard quantum mechanics, the formation of localised solition states is energetically more advantageous than the formation of extended (plane--wave-like or polaron) states (see e.g. /1/ for a review). The question about validity of this statement is not yet finally settled /2/. We are going to question this assertion using trivial variational arguments here. For arbitrary localized standing-soliton state (having its energy lower than the states describing running solitons irrespective of technique used to derive them), we are able to prove the existence of an intermediate or large polaron state whose energy is still lower. Hence, the energy arguments are not sufficient to explain the anomalous soliton stability.