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

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

2009-11-02

arxiv.org/abs/0911.0316v2

Phys. Rev. E83:031130,2011

Nonlinear Sciences

Chaotic Dynamics

8 figures, 8 pages, amplified and corrected, main conclusion unchanged

Scientific paper

10.1103/PhysRevE.83.031130

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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