Duality between the level statistics of Hermitian and non-Hermitian random matrices

arXiv:2609.00162 · cond-mat.stat-mech, cond-mat.mes-hall, quant-ph · Submitted 2026-08-31 · Read on arXiv

cond-mat.stat-mech, cond-mat.mes-hall, quant-ph

Submitted: 2026-08-31

Updated: 2026-09-25

Terminology

• SYK Model — 7× in this paper · explained in 2 episodes
• Decoupling — 5× in this paper · explained in 2 episodes
• Degeneracy — 3× in this paper · explained in 3 episodes
• Effective Hamiltonian — 2× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Random Matrix Theory (RMT) — 1× in this paper · explained in 3 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Non-Hermitian Disordered Systems
• Interpolating non-Hermitian universality classes A and AI$^\dagger$: eigenvalue density and transition regime
• Spectral Density and Eigenvector Nonorthogonality in Complex Symmetric Random Matrices
• Universal spectral correlations in open Floquet systems with localized leaks
• Kac-Rice inspired approach to non-Hermitian random matrices
• Another critique of the replica trick
• Quantum chaotic systems: a random-matrix approach
• Spectral form factor in chaotic, localized, and integrable open quantum many-body systems
• Dissipative Spectral Form Factor of the Complex Elliptic Ginibre Ensemble across Various Non-Hermiticity Regimes

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