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Finding the signature of quantum chaos in experimentally feasible many-body systems is of great interest. In such systems, the spectral form factor (SFF), defined as the Fourier transform of the two-level spectral correlation function, amply demonstrates the behavior of random matrix theory (RMT): a ‘ramp’ followed by a ‘plateau’. It is known that Late. Recently, it was shown that a general initial deviation from the RMT behavior called ‘bump’ exists in random quantum circuits and spin chains as a toy model for many-body quantum chaotic systems. Here we show the existence of a ‘bump-ramp plateau’ behavior in his SFF for many paradigmatic and stroboscopically driven cold atom models of bosons interacting in optical lattices and spinor condensates. It can be seen that the scaling of the many-body Thouless time $t_{\text{Th}}$ (the start time of the (RMT) ramp) and the increase in bump amplitude with atom number differ significantly. In (virtually 0D) chaotic spinor gases, it is slower than in 1D optical lattices, indicating a role of locality in many-body quantum chaos. Moreover, $t_{\text{Th}}$ scaling and bump amplitudes are more sensitive to variations in atomic number than system size, regardless of choice of hyperfine structure, symmetry class, or driving protocol. We obtain a scaling function of the SFF that suggests the power-law behavior of the bump region in a quantum chaotic cold-atom system. Finally, in the lab he proposes an interferometric protocol for probing the SFF.

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