Dissipative Spectral Form Factor of the Complex Elliptic Ginibre Ensemble across Various Non-Hermiticity Regimes (opens in new tab)

We study the dissipative spectral form factor (DSFF) at complex time $T e^{i\theta}$ for the complex elliptic Ginibre ensemble with non-Hermiticity parameter $\tau \in [0,1)$. As the matrix dimension $N \to \infty$, we consider the natural scalings in both the time variable and the non-Hermiticity parameter, namely $T = O(N^\gamma)$ and $1 - \tau = O(N^{-\alpha})$. For all regimes $\gamma \ge 0$ and $\alpha \ge 0$, we derive the precise asympt...