Modeling Disordered Quantum Systems with Dynamical Networks

Details Modeling Disordered Quantum Systems with Dynamical Networks Modeling Disordered Quantum Systems with Dynamical Networks

1999-02-08

arxiv.org/abs/cond-mat/9902100v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

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.

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