Distribution of complex eigenvalues for symplectic ensembles of non-Hermitian matrices

Abstract

Symplectic ensemble of disordered non-Hermitian Hamiltonians is studied. Starting from a model with an imaginary magnetic field, we derive a proper supermatrix $\sigma$-model. The zero-dimensional version of this model corresponds to a symplectic ensemble of weakly non-Hermitian matrices. We derive analytically an explicit expression for the density of complex eigenvalues. This function proves to differ qualitatively from those known for the unitary and orthogonal ensembles. In contrast to these cases, a {\it depletion} of eigenvalues near the real axis occurs. The result about the depletion is in agreement with a previous numerical study performed for QCD models.

15 pages, 1 figure, To appear in Waves in Random Media (special issue on disordered electron systems)

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Cited by in corpus (14)

• Random Matrix Theory and Chiral Symmetry in QCD
• QCD-like Theories at Finite Baryon Density
• Random Matrices close to Hermitian or unitary: overview of methods and results
• Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
• Eigenvalue correlations in non-Hermitean symplectic random matrices
• Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
• Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem
• Random matrices beyond the Cartan classification
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels
• Universal eigenvector correlations in quaternionic Ginibre ensembles
• Universality Conjecture for all Airy, Sine and Bessel Kernels in the Complex Plane
• Random-Matrix Approach to RPA equations. I
• Pfaffian structure of the eigenvector overlap for the symplectic Ginibre ensemble