2002/04/29 by G. Akemann, G Akemann · 1 citation
Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Random Matrices and Applications #cond-mat #hep-th #nlin.CD
paper · pdf · doi:10.1088/0305-4470/36/12/328
published as J.Phys.A36:3363,2003 · 17 pages, 4 figures
arxiv created 2002/04/29 · openalex publication_date 2003/03/13 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
We describe in detail the solution of the extension of the chiral Gaussian unitary ensemble (chGUE) into the complex plane. The correlation functions of the model are first calculated for a finite number of N complex eigenvalues, where we exploit the existence of orthogonal Laguerre polynomials in the complex plane. When taking the large- N limit we derive new correlation functions in the case of weak and strong non-Hermiticity, thus describing the transition from the chGUE to a generalized Ginibre ensemble. We briefly discuss applications to the Dirac operator eigenvalue spectrum in quantum chromodynamics with non-vanishing chemical potential. This is an extended version of hep-th/0204068.