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http://bura.brunel.ac.uk/handle/2438/5084
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. |
URI: | http://bura.brunel.ac.uk/handle/2438/5084 |
Appears in Collections: | Dept of Mathematics Theses Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
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FulltextThesis.pdf | 1.46 MB | Adobe PDF | View/Open |
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