1997/09/30 by Eugene Kanzieper, E. Kanzieper, V. Freilikher · 1 citation
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #Random Matrices and Applications #chao-dyn #cond-mat.dis-nn #cond-mat.stat-mech #hep-th #nlin.CD
paper · pdf · doi:10.1103/physreve.57.6604
published as Physical Review E 57, 6604 (1998) · 12 pages (latex), references added, discussion enlarged
arxiv created 1997/12/23 · openalex publication_date 1998/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of spectra are directly reconstructed from the recurrence equation for orthogonal polynomials associated with a given random matrix ensemble. It is established that an eigenvalue gap does not affect the local eigenvalue correlations that follow the universal sine and the universal multicritical laws in the bulk and soft-edge scaling limits, respectively. By contrast, global smoothed eigenvalue correlations do reflect the presence of a gap, and are shown to satisfy a new universal law exhibiting a sharp dependence on the odd or even dimension of random matrices whose spectra are bounded. In the case of an unbounded spectrum, the corresponding universal ``density-density'' correlator is conjectured to be generic for chaotic systems with a forbidden gap and broken time reversal symmetry.