Abstract. We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average displacement of the walker as a function of time. Indeed, a fast growth of the average displacement can be advantageously exploited to build up efficient search algorithms. By means of analytical and numerical investigations, we show that the finiteness and the inhomogeneity of the substrate jointly weaken the quantum walk performance. We further highlight the interplay between the quantum-walk dynamics and the underlying topology by studying the temporal evolution of the transfer probability distribution and the lower bound of long time averages.

Quantum transport through disordered structures is inhibited by (Anderson) localization effects. The disorder can be either topological as in random networks or energetical as in the original Anderson model. In both cases the eigenstates of the Hamiltonian associated with the network become localized. We show how to overcome localization by network multiplexing. Here, multiple layers of random networks with the same number of nodes are stacked in such a way that in the perpendicular directions regular one-dimensional networks are formed. Depending on the ratio of the coupling within the layer and perpendicular to it, transport gets either enhanced or diminished. In particular, if the couplings are of the same order, transport gets enhanced and localization effects can be overcome. We exemplify our results by two examples: multiplexes of random networks and of one-dimensional Anderson models.

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We investigate the excitonic energy transfer (EET) in the Fenna-Matthews-Olsen complex and obtain the linear absorption spectrum (at 300 K) by a phenomenological time-convolutionless (TCL) master equation which is validated by utilizing Path Integral Monte Carlo (PIMC) simulations. By applying Marcus' theory for choosing the proper Lindblad operators for the longtime incoherent hopping process and using local non-Markovian dephasing rates, our model shows very good agreement with the PIMC results for EET. It also correctly reproduces the linear absorption spectrum that is found in experiment, without using any fitting parameters.

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