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arxiv: cond-mat/0109126 · v2 · submitted 2001-09-06 · ❄️ cond-mat.dis-nn · cond-mat.mes-hall

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Replica treatment of non-Hermitian disordered Hamiltonians

Shinsuke M. Nishigaki , Alex Kamenev (Technion)
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classification ❄️ cond-mat.dis-nn cond-mat.mes-hall
keywords densityensembleshamiltoniansnon-hermitianstatesunitaryapproachborel
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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.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Derivative relations for determinants, Pfaffians and characteristic polynomials in random matrix theory

    math-ph 2026-03 unverdicted novelty 6.0

    Explicit expressions are proven for higher-order and mixed derivatives of determinant and Pfaffian ratios over Vandermonde determinants in random matrix theory.