  We show that the quantum coherent transfer of excitations between
biomolecular chromophores is strongly influenced by spatial correlations of the
environmental fluctuations. The latter are due either to propagating
environmental modes or to local fluctuations with a finite localization length.
A simple toy model of a single donor-acceptor pair with spatially separated
chromophore sites allows to investigate the influence of these spatial
correlations on the quantum coherent excitation transfer. The sound velocity of
the solvent determines the wave lengths of the environmental modes, which, in
turn, has to be compared to the spatial distance of the chromophore sites. When
the wave length exceeds the distance between donor and acceptor site, we find
strong suppression of decoherence. In addition, we consider two spatially
separated donor-acceptor pairs under the influence of propagating environmental
modes. Depending on their wave lengths fixed by the sound velocity of the
solvent material, the spatial range of correlations may extend over typical
interpair distances, which can lead to an increase of the decohering influence
of the solvent. Surprisingly, this effect is counteracted by increasing
temperature.
