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arXiv · 1302.2696

Random reverse-cyclic matrices and screened harmonic oscillator

Shashi C. L. Srivastava·Sudhir R. Jain
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Abstract

We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic oscillator. The connection enables us to obtain all the correlations among the particle positions moving in a screened harmonic potential. The density of nontrivial eigenvalues of this ensemble is found to be of the Wigner form and admits a hole at the origin, in contrast to the semicircle law of the Gaussian orthogonal ensemble of random matrices. The spacing distributions assume different forms ranging from Gaussian-like to Wigner.

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Shashi C. L. Srivastava, Sudhir R. Jain. 2013-02-12. Random reverse-cyclic matrices and screened harmonic oscillator. https://arxiv.org/abs/1302.2696

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