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

TL;DR

This paper discovers a super-exponential growth of out-of-time-ordered correlators (OTOCs) in a nonlinear Schrödinger system, revealing new insights into quantum and classical chaos and information scrambling beyond traditional exponential limits.

Contribution

It introduces a novel super-exponential growth regime of OTOCs in a periodically-modulated nonlinear Schrödinger system, expanding understanding of chaos and information scrambling.

Findings

OTOCs exhibit super-exponential growth in the studied system

Classical hyper-chaos triggers super-EG of classical OTOCs

Results challenge the exponential growth limit in quantum systems

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 Schr\"odinger 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.