MODELING DISORDERED QUANTUM SYSTEMS WITH DYNAMICAL NETWORKS

Rochus Klesse () and Marcus Metzler
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Rochus Klesse: Institut für Theoretische Physik, Universität zu Köln, D-50937 Köln, Germany
Marcus Metzler: Institut für Theoretische Physik, Universität zu Köln, D-50937 Köln, Germany

International Journal of Modern Physics C (IJMPC), 1999, vol. 10, issue 04, 577-606

Abstract: It is the purpose of the present article to show that so-called network models, originally designed to describe static properties of disordered electronic systems, can be easily generalized to quantum-dynamicalmodels, which then allow for an investigation of dynamical and spectral aspects. This concept is exemplified by the Chalker–Coddington model for the quantum Hall effect and a three-dimensional generalization of it. We simulate phase coherent diffusion of wave packets and consider spatial and spectral correlations of network eigenstates as well as the distribution of (quasi-)energy levels. Apart from that, it is demonstrated how network models can be used to determine two-point conductances. Our numerical calculations for the three-dimensional model at the Metal-Insulator transition point delivers, among others, an anomalous diffusion exponent ofη=3-D2=1.7±0.1. The methods presented here in detail have been used partially in earlier work.

Keywords: Anderson localization; Disordered systems; Dynamical systems; Multifractals; Network models; Quantum diffusion; Spectral statistics (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1142/S0129183199000449

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