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We study the quantum dynamics of a photo-excitation uniformly distributed atthe periphery of an extended star network (with $N_B$ branches of length$L_B$). More specifically, we address here the question of the energyabsorption at the core of the network and how this process can be improved (ornot) by the inclusion of peripheral defects with a tunable energy amplitude$\Delta$. Our numerical simulations reveal the existence of optimal value ofenergy defect $\Delta^*$ which depends on the network architecture. Around thisvalue, the absorption process presents a strong speedup (i.e. reduction of theabsorption time) provided that $L_B \leq L_B^*$ with $L_B^* \approx12.5/\ln(N_B) $. Analytical/numerical developments are then conducted tointerpret this feature. We show that the origin of this speedup takes place inthe hybridization of two upper-band excitonic eigenstates. This hybridizationis important when $L_B \leq L_B^*$ and vanishes almost totally when $L_B >L_B^*$. These structural rules we draw here could represent a potential guidefor the practical design of molecular nano-network dedicated to the realisationof efficient photo-excitation absorption.

The extended star graph as a light-harvesting-complex prototype: excitonic absorption speedup by peripheral energy defect tuning