From Davydov solitons to decoherence-free subspaces: self-consistent propagation of coherent-product states

The self-consistent propagation of generalized D1 [coherent-product] states and of a class of Gaussian density-matrix generalizations is examined, at both zero and finite temperature, for arbitrary interactions between the localized lattice (electronic or vibronic) excitations and the phonon modes. It is shown that in all legitimate cases, the evolution of D1 states reduces to the disentangled evolution of the component D2 states. The self-consistency conditions for the latter amount to conditions for decoherence-free propagation, which complement the D2 Davydov soliton equations in such a way as to lift the nonlinearity of the evolution for the on-site degrees of freedom. Although it cannot support Davydov solitons, the coherent-product ansatz does provide a wide class of exact density-matrix solutions for the joint evolution of the lattice and phonon bath in compatible systems. Included are solutions for initial states given as a product of a [largely arbitrary] lattice state and a thermal equilibrium state of the phonons. It is also shown that external pumping can produce self-consistent Frohlich-like effects. A few sample cases of coherent, albeit not solitonic, propagation are briefly discussed.