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

Papenbrock, T.; Pluhar, Z.; Tithof, J.; Weidenmüller, Hans A.

doi:10.1103/PhysRevE.83.031130

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

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Weidenmüller, Hans A.
Prof. Hans A. Weidenmüller, Emeriti, MPI for Nuclear Physics, Max Planck Society;

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0911.0316
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Papenbrock, T., Pluhar, Z., Tithof, J., & Weidenmüller, H. A. (2011). Chaos in fermionic many-body systems and the metal-insulator transition. Physical review E, 83(3): 031130, pp. 1-7. doi:10.1103/PhysRevE.83.031130.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-2EC6-3

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.