Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model

Spectral rigidity in Hermitian quantum chaotic systems signals the presence of dynamical universal features at timescales that can be much shorter than Heisenberg time. We study analog this timescale many-body non-Hermitian chaos by a detailed analysis long-range spectral correlators. For purpose, we investigate number variance and form factor $q$-body Sachdev-Ye-Kitaev (nHSYK) model, which describes $N$ fermions zero spatial dimensions. After an analytical numerical these observables for random matrices, careful unfolding, find good agreement with nHSYK model $q>2$ starting decreases sharply $q$. The source deviation from universality, identified analytically, is ensemble fluctuations not related to dynamics. fixed $q$ large enough $N$, become dominant up until after time, so no longer useful chaos. In all cases, our results point weakened or vanishing effectively delays observation full ergodicity. also show displays nonstationary correlations both matrices. This nonstationarity, dynamics, points intrinsic limitations describe motion. On other hand, introduce local factor, shown stationary affected collective fluctuations, propose it as effective diagnostic $q=2$, saturation Poisson statistics $\mathrm{log}D$, compared scale $\sqrt{D}$ $q>2$, $D$ total states.