Davydov solitons: New results at variance with standard derivations

Abstract

We consider two applications of a method introduced by Davydov for the purpose of modeling energy transport in deformable molecular chains. By specializing to the immobile-exciton limit in which the quantum-mechanical problem is exactly solvable, each application of the method is shown to suffer disagreement with the exact dynamics. Expectation values providing measures of the chain deformation and of the energy content of the chain vibrations are calculated explicitly, as are inner products of model state vectors with corresponding exact state vectors. We show that predictions based on Davydov’s methods may differ substantially from the corresponding exact results under experimentally relevant conditions.