1994/09/27 by Y. Morita, Yusuke Morita, Yasuhiro Hatsugai +3 · 3 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Random Matrices and Applications #Theoretical and Computational Physics #cond-mat #hep-th
paper · pdf · doi:10.1103/physrevb.52.4716
(second revision: authors added)
arxiv created 1994/09/27 · openalex publication_date 1995/08/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 one-dimensional 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.