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Title: A random matrix model for two-colour QCD at non-zero quark density
Authors: Phillips, Michael James
Advisors: Akemann, G
Savin, DV
Keywords: Chiral Ginibre orthogonal ensemble (chGinOE);Non-Hermitian ensemble;Dirac operator;Gluon gauge field;Joint probability density function (JPDF)
Issue Date: 2011
Publisher: Brunel University, School of Information Systems, Computing and Mathematics
Abstract: We solve a random matrix ensemble called the chiral Ginibre orthogonal ensemble, or chGinOE. This non-Hermitian ensemble has applications to modelling particular low-energy limits of two-colour quantum chromo-dynamics (QCD). In particular, the matrices model the Dirac operator for quarks in the presence of a gluon gauge field of fixed topology, with an arbitrary number of flavours of virtual quarks and a non-zero quark chemical potential. We derive the joint probability density function (JPDF) of eigenvalues for this ensemble for finite matrix size N, which we then write in a factorised form. We then present two different methods for determining the correlation functions, resulting in compact expressions involving Pfaffians containing the associated kernel. We determine the microscopic large-N limits at strong and weak non-Hermiticity (required for physical applications) for both the real and complex eigenvalue densities. Various other properties of the ensemble are also investigated, including the skew-orthogonal polynomials and the fraction of eigenvalues that are real. A number of the techniques that we develop have more general applicability within random matrix theory, some of which we also explore in this thesis.
Description: This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University, 17/02/2011.
Appears in Collections:Dept of Mathematics Theses
Mathematical Sciences

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