Quantum transport on honeycomb networks

Abstract

We study the transport properties on honeycomb networks motivated by graphene structures by using the continuous-time quantum walk (CTQW) model. For various relevant topologies we consider the average return probability and its long-time average as measures for the transport efficiency. These quantities are fully determined by the eigenvalues and the eigenvectors of the connectivity matrix of the network. For all networks derived from graphene structures we notice a nontrivial interplay between good spreading and localization effects. Flat graphene with similar number of hexagons along both directions shows a decrease in transport efficiency compared to more one-dimensional structures. This loss can be overcome by increasing the number of layers, thus creating a graphite network, but it gets less efficient when rolling up the sheets so that a nanotube structure is considered. We found peculiar results for honeycomb networks constructed from square graphene, i.e. the same number of hexagons along both directions of the graphene sheet. For these kind of networks we encounter significant differences between networks with an even or odd number of hexagons along one of the axes.

Multiparameter estimation of continuous-time quantum walk Hamiltonians through machine learning

“…CTQWs are especially useful to model physical phenomena such as quantum transport of energy in quantum biological systems, quantum routing, and quantum state transfer. [60][61][62][63][64][65][66] They have been both realized and simulated experimentally on different platforms, such as photons, [67][68][69] trapped atoms and ions, 70,71 waveguide arrays, [72][73][74][75] microwaves, 76 and nuclear magnetic resonance. 77 In all these tasks, fine tuning of the Hamiltonian parameters is required in order to achieve reliable and satisfactory results.…”