Davydov soliton dynamics: two-quantum states and diagonal disorder

Investigation of the dynamics of two-quantum states within Davydov mod D₂) dynamics reveals remarkable differences from one-quantum dynamics. Soliton formation and pinning starts from smaller values of the non-linearity parameter X. From X=30 pN propagating solitons from X=62 pN pinned solitons are observed if both quanta are on the same end of the chain in the initial state. In the case of soliton collisions, the solitons penetrate each other unperturbed for small X, but fuse to a pinned two-quantum soliton for large X. Both one- and two-quantum states are very sensitive to diagonal disorder in the Hamiltonian. In mod D₁) ansatz states, the soliton is found to appear for larger non-linearity but its sensitivity to diagonal disorder is essentially unchanged.