The paper establishes rigorous lower bounds on eigenvector localization lengths for power-law random band matrices in four regimes of the decay exponent α, verifying a physical conjecture via new resolvent techniques.
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Derives precise large-N asymptotics for disconnected and connected DSFF components in the elliptic Ginibre ensemble for all γ ≥ 0, α ≥ 0, characterizing dip-ramp-plateau structures and a mesoscopic interpolating regime.
Derives explicit formulas for mixed spectral moments of complex and symplectic non-Hermitian random matrices in terms of orthogonal polynomial norms, with large-N asymptotics matching elliptic and non-Hermitian Marchenko-Pastur laws.
The paper reviews spectral properties of operators for open quantum evolution and recent theoretical and experimental work on distinguishing chaotic from integrable dissipative quantum systems.
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Localization Lengths of Power-Law Random Band Matrices
The paper establishes rigorous lower bounds on eigenvector localization lengths for power-law random band matrices in four regimes of the decay exponent α, verifying a physical conjecture via new resolvent techniques.