Excitation transfer in a quantum spin model for the photosynthesis process

Biological processes reveal abilities which are very impressive and cannot be adequately explained with the only use of traditional (classical) approaches. A certain amount of quantum mechanics is thought to be used by nature in order to enhance the efficiency of the underlying processes. The question which arises then is: How can quantum features survive in an open quantum system subject to a permanent environmental noise? In this paper we shall present a mathematical model for the illustration of the excitation energy transfer in photosynthesis complexes, with the aim to study the "constructive" interplay between the coherent quantum excitation transfer and the vibrational classical motion of the underlying molecular structure. The model is based on the Schrödinger equation associated to a time-dependent Hamiltonian, describing the propagation of an absorbed photon through a spin-chain towards the reaction center of the photosynthesis apparatus (Spin-Boson model).