Modeling Disordered Quantum Systems with Dynamical Networks

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-{\em dynamical} models, 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 of $\eta =3-D_2=1.7\pm 0.1$. The methods presented here in detail have been used partially in earlier work.

16 pages, Rev-TeX. to appear in Int. J. Mod. Phys. C

References in corpus (5)

• Point-Contact Conductances at the Quantum Hall Transition
• Spatial and Spectral Multifractality of the Local Density of States at the Mobility Edge
• Spectral Properties of the Chalker-Coddington Network
• The Influence of Percolation in the generalized Chalker-Coddington Model
• Spectral Properties of Three Dimensional Layered Quantum Hall Systems

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