139 research outputs found
Layered Chaos in Mean-field and Quantum Many-body Dynamics
We investigate the dimension of the phase space attractor of a quantum
chaotic many-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 regime, and for each of them we
calculate the correlation dimension. For the ground state of the ratchet formed
by a system of field-free non-interacting particles, we find four distinct
pockets of chaotic dynamics throughout these regimes. We show that a
measurement of a local density in each of the dynamical regimes, has an
attractor characterized with a higher fractal dimension, ,
, and , as compared to the global measure
of current, , , and .
We find that the many-body case converges to mean-field limit with strong
sub-unity power laws in particle number , namely with
, and
for each of the dynamical regimes mentioned above.
The deviation between local and global measurement of the attractor's dimension
corresponds to an increase towards high 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 as with
and 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-trapped regimes but not in the chaotic regime.
Based on the obtained results we outline pathways for the identification and
characterization of the emergent phenomena in driven many-body systems
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