Fermionic Mapping For Eigenvalue Correlation Functions Of (Weakly) Non-Hermitian Symplectic Ensemble
Disordered Systems and Neural Networks
2009-10-31 v3
Abstract
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.
Cite
@article{arxiv.cond-mat/9907302,
title = {Fermionic Mapping For Eigenvalue Correlation Functions Of (Weakly) Non-Hermitian Symplectic Ensemble},
author = {M. B. Hastings},
journal= {arXiv preprint arXiv:cond-mat/9907302},
year = {2009}
}
Comments
12 pages, 1 figure, corrected typos. Final published version