Abstract
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
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.
Funder
Studienstiftung des Deutschen Volkes
Engineering and Physical Sciences Research Council
Deutsche Forschungsgemeinschaft
Knut och Alice Wallenbergs Stiftelse
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Reference51 articles.
1. Unquenched complex Dirac spectra at nonzero chemical potential: two-colour QCD lattice data versus matrix model;Akemann;Phys. Rev. Lett.,2006
2. On the determinantal structure of conditional overlaps for the complex Ginibre ensemble;Akemann;Random Matrices: Theory Appl.,2019
3. Universal signature from integrability to chaos in dissipative open quantum systems;Akemann;Phys. Rev. Lett.,2019
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献