We study spectral correlations in many-body quantum mixtures of fermions, bosons, and qubits with periodically kicked spreading and mixing of species. We take two types of mixing, namely, Jaynes-Cummings and Rabi, respectively, satisfying and breaking the conservation of a total number of species. We analytically derive the generating Hamiltonians whose spectral properties determine the spectral form factor in the leading order. We further analyze the system-size $\left(L\right)$ scaling of Thouless time $t^{*}$, beyond which the spectral form factor follows the prediction of random matrix theory. The $L$ dependence of $t^{*}$ crosses over from $lnL$ to $L^2$ with an increasing Jaynes-Cummings mixing between qubits and fermions or bosons in a finite-size chain, and it finally settles to $t^{*}\propto \mathcal{O}\left(L^2\right)$ in the thermodynamic limit for any mixing strength. The Rabi mixing between qubits and fermions leads to $t^{*}\propto \mathcal{O}(lnL)$, previously predicted for single species of qubits or fermions without total-number conservation.

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• Quantum chaos
• Floquet systems
• Quantum chaotic systems
• Random matrix theory