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arXiv · 0911.0316

Chaos in fermionic many-body systems and the metal-insulator transition

T. Papenbrock·Z. Pluhar·J. Tithof·H. A. Weidenmueller
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Abstract

We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are, thus, chaotic. Our argument is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix ensemble ScE that mimics that transition. Our claim then follows from the fact that the generic random-matrix ensemble modeling a fermionic interacting many-body system is much less sparse than ScE.

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T. Papenbrock, Z. Pluhar, J. Tithof, H. A. Weidenmueller. 2009-11-02. Chaos in fermionic many-body systems and the metal-insulator transition. https://doi.org/10.1103/physreve.83.031130

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