Universal Eigenvector Statistics of Non-Hermitian Random Matrices

arXiv:2609.22079 · cond-mat.stat-mech, cond-mat.mes-hall, quant-ph · Submitted 2026-09-18 · Read on arXiv

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

Submitted: 2026-09-18

Updated: 2026-09-18

Terminology

• Degeneracy — 8× in this paper · explained in 3 episodes
• Trace — 7× in this paper · explained in 2 episodes
• SYK Model — 4× in this paper · explained in 2 episodes
• Benchmark — 3× in this paper · explained in 2 episodes
• Calibration — 2× in this paper · explained in 7 episodes
• Effective Hamiltonian — 2× in this paper · explained in 2 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 4 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Random Matrix Theory (RMT) — 1× in this paper · explained in 3 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes

Sources

• Initial-State Typicality in Quantum Relaxation
• Nonergodic extended phase for waves in three dimensions
• Spectral Density and Eigenvector Nonorthogonality in Complex Symmetric Random Matrices
• Duality between the level statistics of Hermitian and non-Hermitian random matrices
• Exact joint eigenvalue densities of non-Hermitian random matrices are Calogero scattering states
• Non-Hermitian Disordered Systems

Related papers

• Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt
• Measurement-induced phase transitions in disordered fermions
• Quantum Thermalization beyond Non-Integrability and Quantum Scars in a Multispecies Bose-Josephson Junction
• Markov length can diverge in systems whose universal physics is spatially Markovian
• Protected domains and cooperative invasion on weighted networks
• Quantum many-body operator cascade as a route to chaos