Evolution of a molecular exciton on a Davydov lattice at<i>T=0</i>

Abstract

We develop a theory of exciton evolution on a zero-temperature Davydov lattice which is free of certain deficiencies found in the standard Davydov theory. The approach makes use of a time-dependent unitary transformation on a Davydov Hamiltonian parametrized by a dimensionless lattice constant a and a dimensionless exciton-phonon coupling constant \ensuremath{\alpha}. The transformation generator is expanded in a normal-ordered series of multiphonon operators with expansion coefficients chosen to eliminate various terms in the transformed Schr\"odinger equation. At the one-phonon level, we obtain equations of motion which differ from those of Davydov. In the small-polaron transportless limit (infinite a) the equations are exact. In the large-polaron continuum limit (vanishing a) the equations become field equations whose stationary solutions are those of Gross's interpolation theory. For a one-spine model of an \ensuremath{\alpha}-helix (a=2.7) we find that soliton formation during evolution from a localized initial state requires a significantly larger value of \ensuremath{\alpha} than is required by Davydov theory.