Replica treatment of non-Hermitian disordered Hamiltonians

Abstract

We employ the fermionic and bosonic replicated nonlinear sigma models to treat Ginibre unitary, symplectic, and orthogonal ensembles of non-Hermitian random matrix Hamiltonians. Using saddle point approach combined with Borel resummation procedure we derive the exact large-N results for microscopic density of states in all three ensembles. We also obtain tails of the density of states as well the two-point function for the unitary ensemble.

REVTeX 3.1, 13 pages, 1 figure; typos fixed (v2)

References in corpus (3)

• Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Replica Treatment of the Calogero-Sutherland Model

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