Fermionic Mapping For Eigenvalue Correlation Functions Of (Weakly) Non-Hermitian Symplectic Ensemble

Details Fermionic Mapping For Eigenvalue Correlation Functions Of (Weakly) Non-Hermitian Symplectic Ensemble Fermionic Mapping For Eigenvalue Correlation Functions Of (Weakly) Non-Hermitian Symplectic Ensemble

1999-07-20

arxiv.org/abs/cond-mat/9907302v3

NPB 572 [FS] 535 (2000)

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 1 figure, corrected typos. Final published version

Scientific paper

10.1016/S0550-3213(00)00043-2

The eigenvalues of an arbitrary quaternionic matrix have a joint probability distribution function first derived by Ginibre. We show that there exists a mapping of this system onto a fermionic field theory and then use this mapping to integrate over the positions of the eigenvalues and obtain eigenvalue density as well as all higher correlation functions for both the strongly and weakly non-Hermitian cases.

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