Geometry of random interactions

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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Cited by in corpus (11)

• The Shell Model as Unified View of Nuclear Structure
• Nuclear Structure, Random Interactions and Mesoscopic Physics
• Regularities of Many-body Systems Interacting by a Two-body Random Ensemble
• Distribution of spectral widths and preponderance of spin-0 ground states in nuclei
• Predominance of Prolate Nuclear Deformations Emerging from Many-Body Interactions
• Bose-Einstein condensates of atoms with arbitrary spin
• Patterns of the ground states in the presence of random interactions: nucleon systems
• Angular momentum I ground state probabilities of boson systems interacting by random interactions
• A study of randomness, correlations and collectivity in the nuclear shell model
• Quadrupole collectivity in random two-body ensembles
• Eigenvalues correlations and the distribution of ground state angular momenta for random many-body quantum systems