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DY: Fachverband Dynamik und Statistische Physik

DY 6: Quantum Dynamics, Decoherence, and Quantum Information I

DY 6.3: Vortrag

Montag, 14. März 2011, 14:30–14:45, ZEU 255

Quantum walk on a star graph with additional bonds — •Anastasiia Anishchenko, Alexander Blumen, and Oliver Mülken — Physikalisches Institut, Albert-Ludwigs Universität Freiburg; Germany

Continuous-time quantum walks (CTQW) are associated with coherent transport processes of, say, energy, mass or charge. CTQW are applicable to many fields of science from polymer physics to quantum computation. It has been shown in [1] that transfer processes depend on the network topology. Here, we concentrate on CTQW on star graphs, a regular structure that consists of N nodes, where the central node has degree N-1 and the other nodes are leaves with degree 1. There are three discrete eigenvalues for the Hamiltonian of such a system: E(1) = E(2) = ... = E(N-2) = 1; E(N-1) = 0; E(N) = N. For the complete graph of size N, where all the nodes are connected, there are two eigenvalues: E(N-1) = 0, and E(N) = N. The periodicity of regular networks such as stars or rings can be destroyed by adding randomly B additional bonds, see, e.g., Ref. [2]. This creates shortcuts, such that a walker can find a shorter way between pairs of sites than on the regular network. In the following we randomly add bonds to regular star graphs forbidding so-called self-connections, and investigate the transition from the regular star graph to the complete graph [3].

[1] O. Mülken, A. Blumen, Phys. Rev. E 71 (2005) 016101.

[2] O. Mülken, V. Pernice, and A. Blumen, Phys. Rev. E 76 (2007) 051125.

[3] A. Anishchenko, A. Blumen, and O. Mülken, in preparation.