Single-particle universality of the many-body spectral form factorFlynn, Michael O. (Avtor) Vidmar, Lev (Avtor) Ikeda, Tatsuhiko N. (Avtor) physicsquantum chaosdisordered systemsWe consider systems of fermions evolved by noninteracting unitary circuits with correlated on-site potentials. When these potentials are drawn from the eigenvalue distribution of a circular random matrix ensemble, the single-particle sector exhibits chaotic dynamics. The corresponding many-body spectral form factors (SFFs) can be computed exactly, revealing signatures of single-particle chaos in the many-body spectral statistics. Due to the absence of interactions the SFF grows exponentially in time, a result which we demonstrate through simple arguments, scaling collapses, and closed-form evaluation of the SFF. Upon introducing interactions, the SFF crosses over to a linear growth regime consistent with many-body random matrix universality. Our exact results for the SFF provide a baseline for future studies of the crossover between single-particle and many-body random matrix behavior.American Physical Society20252026-04-14 10:14:05Neznano28920sl