  We show that the biomolecular exciton dynamics under the influence of slow
polarization fluctuations in the solvent cannot be described by approaches
which are perturbative in the system-bath coupling. For this, we compare
results for the decoherence rate of the exciton dynamics of a resumed
perturbation theory with numerically exact real-time path-integral results. We
find up to one order in magnitude difference in the decoherence rate for
realistically slow solvent environments even in the weak coupling regime, while
both results coincide for fast environmental noise. This shows explicitely the
nonperturbative influence of the bioenvironmental fluctuations and might render
current perturbative approaches to biomolecular exciton transport questionable.
