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Symmetric couplings among aggregates of $n$ chromophores increase thetransfer rate of excitons by a factor $n^2$, a quantum mechanical phenomenoncalled "supertransfer." In this work we demonstrate how supertransfer effectsinduced by geometrical symmetries can enhance the exciton diffusion length by afactor $n$ along cylindrically symmetric structures, consisting of arrays ofrings of chromophores, and along spiral arrays. We analyse both closed systemdynamics and open quantum dynamics, modelled by combining a random bosonic bathwith static disorder. In the closed system case, we use the symmetries of thesystem within a short-time approximation to obtain a closed analyticalexpression for the diffusion length that explicitly reveals the supertransfercontribution. When subject to disorder, we show that supertransfer can enhanceexcitonic diffusion lengths for small disorders and characterize the crossoverfrom coherent to incoherent motion. Owing to the quasi-1D nature of the model,disorder ultimately localizes the excitons, diminishing but not destroying theeffects of supertransfer. When dephasing effects are included, we study thescaling of diffusion with both time and number of chromophores and observe thatthe transition from a coherent, ballistic regime to an incoherent, random-walkregime occurs at the same point as the change from supertransfer to classicalscaling.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Excitonic diffusion length in complex quantum systems: The effects of disorder and environmental fluctuations on symmetry-enhanced supertransfer