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In this study, we explore optimal environments for efficient EET between endsites in a number of dimer and trimer model pigment-protein molecularaggregates when the EET dynamics is modeled by the HEOM-method. For theseoptimal environmental parameters, we further quantify the non-Markovianity bythe BLP-measure to elucidate its possible connection to efficient EET. We alsoquantify coherence in the pigment systems by means of the measure l1-norm ofcoherence to analyze its interplay with environmental effects when EETefficiency is maximal. Our aim is to investigate possible environmental designprinciples for achieving efficient EET in model pigment-protein molecularaggregates and to determine whether non-Markovianity is a possible underlyingresource in such systems. We find that the structure of the system Hamiltonian(i.e., the pigment Hamiltonian parameter space) and especially, therelationship between the site excitation energies, determines whether one oftwo specific environmental regimes is the most beneficial in promotingefficient EET in these model systems. In the first regime, optimalenvironmental conditions are such that the EET dynamics in the system is leftas coherent as possible. In the second regime, the most advantageous role ofthe environment is to drive the system towards equilibrium as fast as possible.In reality, optimal environmental conditions may involve a combination of thesetwo effects. We cannot establish a relation between efficient EET andnon-Markovianity, i.e., non-Markovianity cannot be regarded as a resource inthe systems investigated in this study.

Environmental design principles for efficient excitation energy transfer  in dimer and trimer pigment-protein molecular aggregates and the relation to  non-Markovianity