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

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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.