Dissipative spectral form factor for elliptic Ginibre unitary ensemble and applications

TL;DR

This paper studies the dissipative spectral form factor in the elliptic Ginibre ensemble, revealing how it interpolates between non-Hermitian and Hermitian ensembles, with applications to quantum chaos models and a novel eigenvalue analogy.

Contribution

It derives exact and approximate formulas for the DSFF in eGinUE, connecting it to GinUE and GUE, and explores its implications for quantum chaotic systems and eigenvalue dynamics.

Findings

Derived finite-dimensional and large-size DSFF formulas

Identified scaling relations linking DSFF across ensembles

Validated results with Monte Carlo simulations

Abstract

We investigate the dissipative spectral form factor (DSFF)--a widely used probe of non-Hermitian quantum chaos--in the elliptic Ginibre unitary ensemble (eGinUE), which interpolates between the non-Hermitian Ginibre unitary ensemble (GinUE) and the Hermitian Gaussian unitary ensemble (GUE) via a symmetry breaking parameter. We derive exact finite-dimensional results and large-dimensional approximations for the DSFF, revealing a scaling relationship that connects the DSFF of eGinUE to that of GinUE and the spectral form factor of GUE. This relation explains the distinct time scales underlying the characteristic \emph{dip-ramp-plateau} structure across GinUE, GUE, and crossover regimes. Additionally, we refine estimates of dip-ramp and ramp-plateau transition times for different symmetry regimes. We validate our results with Monte Carlo simulations and demonstrate applications to paradigmatic quantum-chaotic systems: the crossover Sachdev-Ye-Kitaev model and the crossover Power-law Banded random matrices. We highlight an analogy between eGinUE eigenvalues and the positions of a rotating fermionic gas in a two-dimensional anisotropic trap.