Geometry of random interactions
Nuclear Theory
2009-11-10 v1
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.
Cite
@article{arxiv.nucl-th/0301061,
title = {Geometry of random interactions},
author = {P. Chau Huu-Tai and A. Frank and N. A. Smirnova and P. Van Isacker},
journal= {arXiv preprint arXiv:nucl-th/0301061},
year = {2009}
}