Alternative formulation of Davydov’s theory of energy transport in biomolecular systems

Abstract

We consider the system of equations obtained by Davydov from the Fr\"ohlich Hamiltonian through the use of a coherent-state Ansatz. We obtain equations of motion which, although entirely equivalent to the usual Davydov system, allow the dynamics to be analyzed in a more transparent way. In the continuum limit the exact equations reduce to the usual nonlinear Schr\"odinger equation. Initial states and the soliton formation process are discussed, and time and length scales governing soliton coherence properties are determined. In order to address the case of intermediate wavelengths, where the discreteness of the underlying lattice has significant consequences for soliton motion, we formulate a modified nonlinear Schr\"odinger equation which resolves a number of difficulties implicit in the usual nonlinear Schr\"odinger equation.