Super-exponential scrambling of Out-of-time-ordered correlators

Abstract

Out-of-time-ordered correlators (OTOCs) are an effective tool in characterizing black hole chaos, many-body thermalization and quantum dynamics instability. Previous research findings have shown that the OTOCs' exponential growth (EG) marks the limit for quantum systems. However, we report in this letter a periodically-modulated nonlinear Schrödinger system, in which we interestingly find a novel way of information scrambling: super-EG. We show that the quantum OTOCs' growth, which stems from the quantum chaotic dynamics, will increase in a super-exponential way. We also find that in the classical limit, the hyper-chaos revealed by a linearly-increasing Lyapunov exponent actually triggers the super-EG of classical OTOCs. The results in this paper break the restraints of EG as the limit for quantum systems, which give us new insight into the nature of information scrambling in various fields of physics from black hole to many-body system.

6 pages, 3 figures

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• Relating out-of-time-order correlations to entanglement via multiple-quantum coherences
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Cited by in corpus (12)

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• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in a Floquet system
• Low temperature quantum bounds on simple models
• Quantum algorithm for evaluating operator size with Bell measurements
• Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
• Manifestation of strange nonchaotic attractors in extended systems: A study through out-of-time-ordered correlators
• Quantum Signatures of Chaos in Anisotropic Quantum Rabi Model
• Revealing quantum operator scrambling via measuring Holevo information on digital quantum simulators
• Emergent dynamical quantum phase transition in a $Z_3$ symmetric chiral clock model
• Long-time signatures of chaos in large atom-light frequency ratios Rabi model