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Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the Ehrenfest timescale
Published in APS
2020
Volume: 101
   
Issue: 12
Abstract
Out-of-time-order correlators (OTOCs), vigorously being explored as a measure of quantum chaos and information scrambling, is studied here in the natural and simplest multiparticle context of bipartite systems. We show that two strongly chaotic and weakly interacting subsystems display two distinct regimes in the growth of OTOCs. The first is dominated by intrasubsystem scrambling, when an exponential growth with a positive Lyapunov exponent is observed until the Ehrenfest time. This regime is essentially independent of the interaction, while the second one is an interaction dominated exponential approach to saturation that is universal and described by a random matrix model. This simple random matrix model of weakly interacting strongly chaotic bipartite systems, previously employed for studying entanglement and spectral transitions, is approximately analytically solvable for its OTOC. The example of two coupled kicked rotors is used to demonstrate the different regimes, and the extent to which the random matrix model is applicable. We remark that the second regime implies an emergent invariance of the OTOC under local unitary transformations suggesting that the rate of relaxation is connected to the entangling power of the interaction. That the two regimes correspond to delocalization in the subsystems followed by intersubsystem mixing is seen via the participation ratio in phase space. We also point out that the second, universal, regime alone exists when the observables are in a sense locally prescrambled. © 2020 American Physical Society.
About the journal
JournalPhysical Review B
PublisherAPS
ISSN24699950
Open AccessNo