1998/09/14 by A. V. Kolesnikov, K. B. Efetov
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #cond-mat.dis-nn #hep-lat #hep-th
paper · pdf · doi:10.1088/0959-7174/9/2/301
published as Waves Random Media 9 (1999) 71 · 15 pages, 1 figure, To appear in Waves in Random Media (special issue on disordered electron systems)
arxiv created 1998/09/14 · openalex publication_date 1999/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
A symplectic ensemble of disordered non-Hermitian Hamiltonians is studied. Starting from a model with an imaginary magnetic field, we derive a proper supermatrix σ-model. The zero-dimensional version of this model corresponds to a symplectic ensemble of weakly non-Hermitian 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.