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In an extended star with peripheral defects and a core occupied by a trap, ithas been shown that exciton-mediated energy transport from the periphery to thecore can be optimized [S. Yalouz et al. Phys. Rev. E 106, 064313 (2022)]. Ifthe defects are judiciously chosen, the exciton dynamics is isomorphic to thatof an asymmetric chain and a speedup of the excitonic propagation is observed.Here, we extend this previous work by considering that the exciton in both anextended star and an asymmetric chain, is perturbed by the presence of adephasing environment. Simulating the dynamics using a Lindblad masterequation, two questions are addressed: how does the environment affect theenergy transport on these two networks? And, do the two systems still behaveequivalently in the presence of dephasing? Our results reveal that thetime-scale for the exciton dynamics strongly depends on the nature of thenetwork. But quite surprisingly, the two networks behave similarly regardingthe survival of their optimization law. In both cases, the energy transport canbe improved using the same original optimal tuning of energy defects as long asthe dephasing remains weak. However, for moderate/strong dephasing, theoptimization law is lost due to quantum Zeno effect.

Optimized excitonic transport mediated by local energy defects: survival of optimization laws in the presence of dephasing