Correlations of Eigenvectors for Non-Hermitian Random-Matrix Models
arXiv:cond-mat/9902314 · doi:10.1103/PhysRevE.60.2699
Abstract
We establish a general relation between the diagonal correlator of eigenvectors and the spectral Green's function for non-hermitian random-matrix models in the large-N limit. We apply this result to a number of non-hermitian random-matrix models and show that the outcome is in good agreement with numerical results.
10 pages with 4 EPS figures included
References in corpus (7)
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- Non-Hermitean Random Matrix Theory: method of hermitization
- Eigenvector statistics in non-Hermitian random matrix ensembles
- Directed Quantum Chaos
- Non-Gaussian Non-Hermitean Random Matrix Theory: phase transitions and addition formalism
- Quantum Disordered Systems with a Direction
- Diffusion in a Random Velocity Field: Spectral Properties of a Non-Hermitian Fokker-Planck Operator
Cited by in corpus (48)
- Random Matrices close to Hermitian or unitary: overview of methods and results
- Universal spectra of random Lindblad operators
- Statistical properties of eigenvectors in non-Hermitian Gaussian random matrix ensembles
- Non-Hermitian Euclidean random matrix theory
- Spectral Theory of Sparse Non-Hermitian Random Matrices
- On the statistics of resonances and non-orthogonal eigenfunctions in a model for single-channel chaotic scattering
- Symmetry Classification of Many-Body Lindbladians: Tenfold Way and Beyond
- Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem
- The distribution of overlaps between eigenvectors of Ginibre matrices
- On statistics of bi-orthogonal eigenvectors in real and complex Ginibre ensembles: combining partial Schur decomposition with supersymmetry
- Dysonian dynamics of the Ginibre ensemble
- Infinite Products of Large Random Matrices and Matrix-valued Diffusion
- Resonances in open quantum maps
- Delocalization of eigenvectors of random matrices with independent entries
- Quantum-limited linewidth of a chaotic laser cavity
- Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
- Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem
- Multiplication law and S transform for non-hermitian random matrices
- "Single Ring Theorem" and the Disk-Annulus Phase Transition
- Eigenvalues of non-hermitian random matrices and Brown measure of non-normal operators: hermitian reduction and linearization method
- 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
- Condition numbers for real eigenvalues in the real Elliptic Gaussian ensemble
- Critical statistics for non-Hermitian matrices
- A Note on Mixed Matrix Moments for the Complex Ginibre Ensemble
- A model for chaotic dielectric microresonators
- Eigenvalue spectra of large correlated random matrices
- Universal hypotrochoidic law for random matrices with cyclic correlations
- From synaptic interactions to collective dynamics in random neuronal networks models: critical role of eigenvectors and transient behavior
- Universal eigenvector statistics in a quantum scattering ensemble
- Full Dysonian dynamics of the complex Ginibre ensemble
- Spectra of large time-lagged correlation matrices from Random Matrix Theory
- Impact of non-Hemiticity on modal strength and correlation in transmission through random open cavities
- Chaotic Scattering with Localized Losses: S-Matrix Zeros and Reflection Time Difference for Systems with Broken Time Reversal Invariance
- Eigenvector statistics of the product of Ginibre matrices
- Top Eigenpair Statistics for Weighted Sparse Graphs
- Reflection Time Difference as a probe of S-matrix Zeroes in Chaotic Resonance Scattering
- Summing free unitary random matrices
- Spectrum of non-Hermitian deep-Hebbian neural networks
- Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities
- Eikonal formulation of large dynamical random matrix models
- Ornstein-Uhlenbeck diffusion of hermitian and non-hermitian matrices - unexpected links
- Quaternionic R transform and non-hermitian random matrices
- Complete diagrammatics of the single ring theorem
- Condition numbers for real eigenvalues of real elliptic ensemble: weak non-normality at the edge
- Pfaffian structure of the eigenvector overlap for the symplectic Ginibre ensemble
- Optimal Fluctuations and Tail States of non-Hermitian Operators
- Eigenvalue and pseudospectrum processes generated by nonnormal Toeplitz matrices with rank 1 perturbations