Distribution of complex eigenvalues for symplectic ensembles of nonHermitian matrices
Abstract
A symplectic ensemble of disordered nonHermitian Hamiltonians is studied. Starting from a model with an imaginary magnetic field, we derive a proper supermatrix icons/Journals/Common/sigma" ALT="sigma" ALIGN="TOP"/>model. The zerodimensional version of this model corresponds to a symplectic ensemble of weakly nonHermitian matrices. We derive analytically an explicit expression for the density of complex eigenvalues. This function proves to differ qualitatively from those known for the unitary and orthogonal ensembles. In contrast to these cases, a depletion of the eigenvalues occurs near the real axis. The result about the depletion is in agreement with a previous numerical study performed for QCD models.
 Publication:

Waves in Random Media
 Pub Date:
 April 1999
 DOI:
 10.1088/09597174/9/2/301
 arXiv:
 arXiv:condmat/9809173
 Bibcode:
 1999WRM.....9...71K
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 15 pages, 1 figure, To appear in Waves in Random Media (special issue on disordered electron systems)