Universal Correlations in the random matrices and 1D particles with long range interactions in a confinement potential

Details Universal Correlations in the random matrices and 1D particles with long range interactions in a confinement potential Universal Correlations in the random matrices and 1D particles with long range interactions in a confinement potential

1994-09-26

arxiv.org/abs/cond-mat/9409110v2

Physics

Condensed Matter

(second revision: authors added)

Scientific paper

10.1103/PhysRevB.52.4716

We study the correlations between eigenvalues of the large random matrices by a renormalization group approach. The results strongly support the universality of the correlations proposed by Br\'ezin and Zee. Then we apply the results to the ground state of the 1D particles with long range interactions in a confinement potential. We obtain the exact ground state. We also show the existence of a transition similar to a phase separation. Before and after the transition, we obtain the density-density correlation explicitly. The correlation shows nontrivial universal behavior.

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