Layered chaos in mean-field and quantum many-body dynamics

We investigate the dimension of the phase-space attractor of a quantum chaoticmany-body ratchet in the mean-field limit. Specifically, we explore a driven Bose-Einstein condensate in three distinct dynamical regimes-Rabi oscillations, chaos, and self-trapping regimes-and for each of them we calculate the correlation dimension. For the ground state of the ratchet formed by a system of field-free noninteracting particles, we find four distinct pockets of chaotic dynamics throughout these regimes. We show that a measurement of local density in each of the dynamical regimes has an attractor characterized by a higher fractal dimension, D-R = 2.59 +/- 0.01, D-C = 3.93 +/- 0.04, and D-S = 3.05 +/- 0.05, compared to the globalmeasure of current, D-R = 2.07 +/- 0.02, D-C = 2.96 +/- 0.05, and D-S = 2.30 +/- 0.02. The deviation between local and global measurements of the attractor's dimension corresponds to an increase towards higher condensate depletion, which remains constant for long time scales in both Rabi and chaotic regimes. The depletion is found to scale polynomially with particle number N, namely, as N-beta with beta(R) = 0.51 +/- 0.004 and beta(C) = 0.18 +/- 0.004 for the two regimes. Thus, we find a strong deviation from the mean-field results, especially in the chaotic regime of the quantum ratchet. The ratchet also reveals quantum revivals in the Rabi and self-trapping regimes but not in the chaotic regime, with revival times scaling linearly in particle number for Rabi dynamics. Based on the obtained results, we outline pathways for the identification and characterization of emergent phenomena in driven many-body systems. This includes the identification of many-body localization from the many-body measures of the system, the influence of entanglement on the rate of the convergence to the mean-field limit, and the establishment of a polynomial scaling of the Ehrenfest time at which the mean-field description fails to describe the dynamics of the system.