The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor in coupled bipartite chaotic quantum systems and obtain all moments of the spectral form factor exactly in the semiclassical limit of large Hilbert space dimension. Extrapolating those results to finite Hilbert space dimension we find a universal dependence of the spectral form factor on a single scaling parameter for times larger than the subsystem’s Heisenberg time. We complement our analysis by a perturbative approach covering the small coupling regime. Our results are derived in a random matrix model adapted to the bipartite nature of our setting in which we find excellent agreement between analytical results and extensive numerical studies. Moreover, we demonstrate that our results apply equally well to actual bipartite chaotic quantum systems by accurately describing the spectral form factor and its universal dependence on the scaling parameter in quantized coupled kicked rotors. Ultimately, we discuss an extension of our results to the many-body setting.

* Felix Fritzsch, FMF, University of Ljubljana