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Geometry of random interactions

P. Chau Huu-Tai·A. Frank·N. A. Smirnova·P. Van Isacker
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Abstract

It is argued that spectral features of quantal systems with random interactions can be given a geometric interpretation. This conjecture is investigated in the context of two simple models: a system of randomly interacting d bosons and one of randomly interacting fermions in a j=7/2 shell. In both examples the probability for a given state to become the ground state is shown to be related to a geometric property of a polygon or polyhedron which is entirely determined by particle number, shell size, and symmetry character of the states. Extensions to more general situations are discussed.

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P. Chau Huu-Tai, A. Frank, N. A. Smirnova, P. Van Isacker. 2003-01-21. Geometry of random interactions. https://doi.org/10.1103/physrevc.66.061302

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