Berlin 2008 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Poster I

DY 17.12: Poster

Tuesday, February 26, 2008, 16:00–18:00, Poster C

Quantum transport on small-world networks: A continuous-time quantum walk approach — Oliver Mülken, •Volker Pernice, and Alexander Blumen — Theoretische Polymerphysik, Universität Freiburg, D-79104 Freiburg

We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWN). The SWN are built from a one-dimensional ring of N nodes by randomly introducing B shortcuts in the form of additional bonds between them.

The exciton dynamics is modeled by continuous-time quantum walks, a quantum mechanical analog of continuous-time random walks. We evaluate numerically the ensemble averaged transition probability to reach any node of the network from the initially excited one. We observe that already a few connections obliterate the pattern of quantum carpets that is present for transport on a ring.

For sufficiently large B we find that the quantum mechanical transport through the SWN is, first, very fast, given that a limiting distribution of the transition probabilities is reached very quickly; second, that in contrast to the classical case, where the limiting value is 1/N for all nodes, the transport does not lead to equipartition, given that on average the exciton is most likely to be found at the initial node. The reason for this is to be found in the network’s eigenstates, which are localized at the band edges, whereas inside the band they are quite delocalized, similar to the undisturbed network [1].

[1] O.Mülken, V.Pernice, A.Blumen, Phys. Rev. E (2007) in press