Dresden 2006 – scientific programme

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DY: Dynamik und Statistische Physik

DY 46: Poster

DY 46.85: Poster

Thursday, March 30, 2006, 16:00–18:00, P1

CONTINUOUS TIME QUANTUM WALKS ON TWO-DIMENSIONAL NETWORKS — •Antonio Volta, Oliver Mülken, and Alexander Blumen — Theoretische Polymerphysik, Universität Freiburg, Hermann Herder Straße 3, 79104 Freiburg, Germany

We present a description of the quantum mechanical transport by continuous time quantum walks (CTQWs) on networks topologically equivalent to two-dimensional lattices. The quantum transport topic increased recently its importance because of the development of quantum information theory and the application to potential quantum computers. We provide results for CTQW on discrete tori, cylinders and finite squares. The propagation is described by the Schrödinger equation. In the case of finite square lattices, by placing at time t=0 the excitation in one corner, one observes a very fast transport to the opposite one via the diagonal. The long time average of the transition probability distribution shows, for some special lattice sizes, asymmetric features. We also pay attention to the probability to be still or again at the initial site. We provide, for the quantum mechanical case, a lower bound which for some geometries is rather close to the exact, numerical result. The lower bound depends only on the eigenvalue spectrum of the Hamiltonian, which can be obtained analytically for our structures, by applying methods from solid state and polymer physics.

[1] O. Mülken, A. Volta, A. Blumen, Phys. Rev. A 72 (2005) 042334