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arXiv · 2606.20824

Parametric correlations in non-Hermitian quantum chaos: random matrix approach

Yan V. Fyodorov·Bertrand Lacroix-A-Chez-Toine
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Abstract

Motivated by the surge of interest in statistics of non-Hermitian random matrices as a framework for description of universal characteristics of dissipative chaotic quantum many-body systems, we address the problem of characterizing the parametric correlations of spectral densities. Considering parameter-dependent ensemble of complex Ginibre matrices we derive an explicit, closed-form expression for the parametric number covariance in the systems of symmetry class $\mathbf{A}$ for eigenvalues in a circular domain containing on average a finite number of eigenvalues in the spectral bulk. This behavior is expected to be universal, as further supported by numerical evidence for the real Ginibre ensemble, non-Hermitian Bernoulli Wigner matrices and bi-unitarily invariant ensembles. We also discuss a relation between parametric correlations of spectral densities and the distribution of the so-called eigenvector non-orthogonality factor, which attracted considerable interest in recent years.

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Yan V. Fyodorov, Bertrand Lacroix-A-Chez-Toine. 2026-06-18. Parametric correlations in non-Hermitian quantum chaos: random matrix approach. https://arxiv.org/abs/2606.20824

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