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DC Field | Value | Language |
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dc.contributor.advisor | Akemann, G | - |
dc.contributor.advisor | Savin, DV | - |
dc.contributor.author | Phillips, Michael James | - |
dc.date.accessioned | 2011-04-27T12:38:54Z | - |
dc.date.available | 2011-04-27T12:38:54Z | - |
dc.date.issued | 2011 | - |
dc.identifier.uri | http://bura.brunel.ac.uk/handle/2438/5084 | - |
dc.description | This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University, 17/02/2011. | en_US |
dc.description.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. | en_US |
dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) | en_US |
dc.language.iso | en | en_US |
dc.publisher | Brunel University, School of Information Systems, Computing and Mathematics | - |
dc.relation.ispartof | School of Information Systems, Computing and Mathematics | - |
dc.relation.uri | http://bura.brunel.ac.uk/bitstream/2438/5084/1/FulltextThesis.pdf | - |
dc.subject | Chiral Ginibre orthogonal ensemble (chGinOE) | en_US |
dc.subject | Non-Hermitian ensemble | en_US |
dc.subject | Dirac operator | en_US |
dc.subject | Gluon gauge field | en_US |
dc.subject | Joint probability density function (JPDF) | en_US |
dc.title | A random matrix model for two-colour QCD at non-zero quark density | en_US |
dc.type | Thesis | en_US |
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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