Self-trapping on a dimer: Time-dependent solutions of a discrete nonlinear Schrödinger equation

From the discrete nonlinear Schr\"odinger equation describing transport on a dimer we derive and solve a closed nonlinear equation for the site-occupation probability difference. Our results, which are directly relevant to specific experiments such as neutron scattering in physically realizable dimers, exhibit a transition from "free" to "self-trapped" behavior and illustrate features expected in extended systems, including soliton/polaron bandwidth reduction and the dependence of energy-transfer efficiency on initial conditions.