Finite Size Corrections to the Excitation Energy Transfer in a Massless Scalar Interaction Model

We study the excitation energy transfer (EET) for a simple model in which a massless scalar particle is exchanged between two molecules. We show that a finite-size effect appears in EET by the interaction energy due to overlapping of the quantum waves in a short time interval. The effect generates finite-size corrections to Fermi's golden rule and modifies EET probability from the standard formula in the Forster mechanism. The correction terms come from transition modes outside the resonance energy region and enhance EET probability substantially.