Universal eigenvector correlations in quaternionic Ginibre ensembles

Abstract

Non-Hermitian random matrices enjoy non-trivial correlations in the statistics of their eigenvectors. We study the overlap among left and right eigenvectors in Ginibre ensembles with quaternion valued Gaussian matrix elements. This concept was introduced by Chalker and Mehlig in the complex Ginibre ensemble. Using a Schur decomposition, for harmonic potentials we can express the overlap in terms of complex eigenvalues only, coming in conjugate pairs in this symmetry class. Its expectation value leads to a Pfaffian determinant, for which we explicitly compute the matrix elements for the induced Ginibre ensemble with $2\alpha$ zero eigenvalues, for finite matrix size $N$. In the macroscopic large-$N$ limit in the bulk of the spectrum we recover the limiting expressions of the complex Ginibre ensemble for the diagonal and off-diagonal overlap, which are thus universal.

arXiv comment26 pages; v2: references added and typos corrected; v3: more references added and typos corrected

References in corpus (26)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Eigenvector statistics in non-Hermitian random matrix ensembles
• Random Matrices close to Hermitian or unitary: overview of methods and results
• The Ginibre ensemble of real random matrices and its scaling limits
• Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
• Large N expansion for the 2D Dyson gas
• Quantum limit of the laser linewidth in chaotic cavities and statistics of residues of scattering matrix poles
• Statistics of resonance width shifts as a signature of eigenfunction non-orthogonality
• Statistical properties of eigenvectors in non-Hermitian Gaussian random matrix ensembles
• Eigenvalue correlations in non-Hermitean symplectic random matrices
• On the statistics of resonances and non-orthogonal eigenfunctions in a model for single-channel chaotic scattering
• Induced Ginibre ensemble of random matrices and quantum operations
• On statistics of bi-orthogonal eigenvectors in real and complex Ginibre ensembles: combining partial Schur decomposition with supersymmetry
• Large Petermann factor in chaotic cavities with many scattering channels
• Experimental Width Shift Distribution: A Test of Nonorthogonality for Local and Global Perturbations
• Dysonian dynamics of the Ginibre ensemble
• Delocalization of eigenvectors of random matrices with independent entries
• Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem
• Unveiling the significance of eigenvectors in diffusing non-hermitian matrices by identifying the underlying Burgers dynamics
• Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach
• A Note on Mixed Matrix Moments for the Complex Ginibre Ensemble
• Distribution of complex eigenvalues for symplectic ensembles of non-Hermitian matrices
• Unquenched complex Dirac spectra at nonzero chemical potential: two-colour QCD lattice data versus matrix model
• On characteristic polynomials for a generalized chiral random matrix ensemble with a source
• Eigenvector statistics of the product of Ginibre matrices
• Fermionic Mapping For Eigenvalue Correlation Functions Of (Weakly) Non-Hermitian Symplectic Ensemble

Cited by in corpus (4)

• Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities
• Pfaffian structure of the eigenvector overlap for the symplectic Ginibre ensemble
• Condition numbers for real eigenvalues of real elliptic ensemble: weak non-normality at the edge
• New term in effective field theory at fixed topology