Universal eigenvector correlations in quaternionic Ginibre ensembles

Akemann G, Forster Y-P, Kieburg M (2020)
Journal of Physics A, Mathematical and Theoretical 53(14): 145201.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Akemann, GernotUniBi; Forster, Yanik-Pascal; Kieburg, Mario
Abstract / Bemerkung
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.
Stichworte
eigenvector statistics; quaternionic Ginibre ensemble; universality
Erscheinungsjahr
2020
Zeitschriftentitel
Journal of Physics A, Mathematical and Theoretical
Band
53
Ausgabe
14
Art.-Nr.
145201
ISSN
1751-8113
eISSN
1751-8121
Page URI
https://pub.uni-bielefeld.de/record/2942715

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Akemann G, Forster Y-P, Kieburg M. Universal eigenvector correlations in quaternionic Ginibre ensembles. Journal of Physics A, Mathematical and Theoretical. 2020;53(14): 145201.
Akemann, G., Forster, Y. - P., & Kieburg, M. (2020). Universal eigenvector correlations in quaternionic Ginibre ensembles. Journal of Physics A, Mathematical and Theoretical, 53(14), 145201. doi:10.1088/1751-8121/ab766e
Akemann, G., Forster, Y. - P., and Kieburg, M. (2020). Universal eigenvector correlations in quaternionic Ginibre ensembles. Journal of Physics A, Mathematical and Theoretical 53:145201.
Akemann, G., Forster, Y.-P., & Kieburg, M., 2020. Universal eigenvector correlations in quaternionic Ginibre ensembles. Journal of Physics A, Mathematical and Theoretical, 53(14): 145201.
G. Akemann, Y.-P. Forster, and M. Kieburg, “Universal eigenvector correlations in quaternionic Ginibre ensembles”, Journal of Physics A, Mathematical and Theoretical, vol. 53, 2020, : 145201.
Akemann, G., Forster, Y.-P., Kieburg, M.: Universal eigenvector correlations in quaternionic Ginibre ensembles. Journal of Physics A, Mathematical and Theoretical. 53, : 145201 (2020).
Akemann, Gernot, Forster, Yanik-Pascal, and Kieburg, Mario. “Universal eigenvector correlations in quaternionic Ginibre ensembles”. Journal of Physics A, Mathematical and Theoretical 53.14 (2020): 145201.

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arXiv: 1911.12032

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