Geometry of random interactions

Details Geometry of random interactions Geometry of random interactions

2003-01-21

arxiv.org/abs/nucl-th/0301061v1

Phys.Rev. C66 (2002) 061302

Physics

Nuclear Physics

Nuclear Theory

Scientific paper

10.1103/PhysRevC.66.061302

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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