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 = 72 shell. In both examples the probability for a specific state to become the ground state is shown to be related to a geometric property of a (hyper)polyhedron which is interaction‐independent and is determined solely by particle number, shell size and symmetry character of the state. Extensions of these ideas to more general situations are discussed.
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