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Title:  The complex laguerre symplectic ensemble of NonHermitian matrices 
Authors:  Akemann, G 
Keywords:  High energy physics  theory Mathematical physics Mesoscopic systems and quantum hall effect 
Publication Date:  2005 
Publisher:  Elsevier 
Citation:  Nuclear Physics B, 730(3): 253299, Jul 2005 
Abstract:  We solve the complex extension of the chiral Gaussian Symplectic Ensemble, defined as a Gaussian twomatrix model of chiral nonHermitian quaternion real matrices. This leads to the appearance of Laguerre polynomials in the complex plane and we prove their orthogonality. Alternatively, a complex eigenvalue representation of this ensemble is given for general weight functions. All kpoint correlation functions of complex eigenvalues are given in terms of the corresponding skew orthogonal polynomials in the complex plane for finiteN, where N is the matrix size or number of eigenvalues, respectively. We also allow for an arbitrary number of complex conjugate pairs of characteristic polynomials in the weight function, corresponding to massive quark flavours in applications to field theory. Explicit expressions are given in the largeN limit at both weak and strong nonHermiticity for the weight of the Gaussian twomatrix model. This model can be mapped to the complex Dirac operator spectrum with nonvanishing chemical potential. It belongs to the symmetry class of either the adjoint representation or two colours in the fundamental representation using staggered lattice fermions. 
URI:  http://bura.brunel.ac.uk/handle/2438/449 
DOI:  http://dx.doi.org/10.1016/j.nuclphysb.2005.09.039 
Appears in Collections:  School of Information Systems, Computing and Mathematics Research Papers Mathematical Science

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