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

• URL: http://arxiv.org/abs/2606.20824v1
• Date: Thu, 18 Jun 2026 18:09:35 GMT
• Title: Parametric correlations in non-Hermitian quantum chaos: random matrix approach
• Abstract summary: We discuss the problem of characterizing the parametric correlations of spectral densities.<n>We derive an explicit, closed-form expression for the parametric number covariance in the systems of symmetry class $mathbfA$ for eigenvalues.<n>We also discuss a relation between parametric correlations of spectral densities and the distribution of the so-called eigenvector non-orthogonality factor.
• Score: 28.023703674946223
• License: http://creativecommons.org/licenses/by/4.0/
• 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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