We show that Out-of-Time-Ordered Correlator (OTOC) growth in the Quantum Kicked Rotor (QKR) quantifies information scrambling rather than entropy production. Numerical simulations reproduce the quadratic OTOC scaling at resonance (ℏeff=4π) and its suppression under detuning. Bitstreams derived from the evolving wavefunction reveal a nonmonotonic relationship between chaos and entropy: the resonant (maximally chaotic) regime exhibits lower measured entropy due to coherent phase correlations, whereas slight detuning enhances statistical uniformity. While Out-of-Time-Ordered Correlators quantify information scrambling rather than entropy production, we show that the strength of scrambling strongly constrains the amount of classical entropy that can be extracted after measurement.
We show that Out-of-Time-Ordered Correlator (OTOC) growth in the Quantum Kicked Rotor (QKR) quantifies information scrambling rather than entropy production. Numerical simulations reproduce the quadratic OTOC scaling at resonance (ℏeff=4π) and its suppression under detuning. Bitstreams derived from the evolving wavefunction reveal a nonmonotonic relationship between chaos and entropy: the resonant (maximally chaotic) regime exhibits lower measured entropy due to coherent phase correlations, whereas slight detuning enhances statistical uniformity. While Out-of-Time-Ordered Correlators quantify information scrambling rather than entropy production, we show that the strength of scrambling strongly constrains the amount of classical entropy that can be extracted after measurement.
We investigate both theoretically and numerically the dynamics of out-of-time-ordered correlators (OTOCs) in quantum resonance conditions for a kicked rotor model. We employ various operators to construct OTOCs in order to thoroughly quantify their commutation relation at different times, therefore unveiling the process of quantum scrambling. With the help of quantum resonance condition, we have deduced the exact expressions of quantum states during both forward evolution and time reversal, which enables us to establish the laws governing OTOCs' time dependence. We find interestingly that the OTOCs of different types increase in a quadratic function of time, breaking the freezing of quantum scrambling induced by the dynamical localization under non-resonance condition. The underlying mechanism is discovered, and the possible applications in quantum entanglement are discussed.
While classical chaos has been successfully characterized with consistent theories and intuitive techniques, such as with the use of Lyapunov exponents, quantum chaos is still poorly understood, as well as its relation with multi-partite entanglement and information scrambling. We consider a benchmark system, the kicked top model, which displays chaotic behaviour in the classical version, and proceed to characterize the quantum case with a thorough diagnosis of the growth of chaos and entanglement in time. As a novel tool for the characterization of quantum chaos, we introduce for this scope the quasi-probability distribution behind the out-of-time-ordered correlator (OTOC). We calculate the cumulative nonclassicality of this distribution, which has already been shown to outperform the simple use of OTOC as a probe to distinguish between integrable and nonintegrable Hamiltonians. To provide a thorough comparative analysis, we contrast the behavior of the nonclassicality with entanglement measures, such as the tripartite mutual information of the Hamiltonian as well as the entanglement entropy. We find that systems whose initial states would lie in the "sea of chaos" in the classical kicked-top model, exhibit, as they evolve in time, characteristics associated with chaotic behavior and entanglement production in closed quantum systems. We corroborate this indication by capturing it with this novel OTOC-based measure.
We study operator growth in a bipartite kicked coupled tops (KCTs) system using out-of-time ordered correlators (OTOCs), which quantify "information scrambling" due to chaotic dynamics and serve as a quantum analog of classical Lyapunov exponents. In the KCT system, chaos arises from the hyper-fine coupling between the spins. Due to a conservation law, the system's dynamics decompose into distinct invariant subspaces. Focusing initially on the largest subspace, we numerically verify that the OTOC growth rate aligns well with the classical Lyapunov exponent for fully chaotic dynamics. While previous studies have largely focused on scrambling in fully chaotic dynamics, works on mixed-phase space scrambling are sparse. We explore scrambling behavior in both mixed-phase space and globally chaotic dynamics. In the mixed-phase space, we use Percival's conjecture to partition the eigenstates of the Floquet map into "regular" and "chaotic." Using these states as the initial states, we examine how their mean phase space locations affect the growth and saturation of the OTOCs. Beyond the largest subspace, we study the OTOCs across the entire system, including all other smaller subspaces. For certain initial operators, we analytically derive the OTOC saturation using random matrix theory (RMT). When the initial operators are chosen randomly from the unitarily invariant random matrix ensembles, the averaged OTOC relates to the linear entanglement entropy of the Floquet operator, as found in earlier works. For the diagonal Gaussian initial operators, we provide a simple expression for the OTOC.
We investigate both numerically and analytically the dynamics of out-of-time-order correlators (OTOCs) in a non-Hermitian kicked rotor model, addressing the scaling laws of the time dependence of OTOCs at the transition to the spontaneous PT-symmetry breaking. In the unbroken phase of PT symmetry, the OTOCs increase monotonically and eventually saturate with time, demonstrating the freezing of information scrambling. Just beyond the phase transition points, the OTOCs increase in the power laws of time, with the exponent being larger than 2. Interestingly, the quadratic growth of OTOCs with time emerges when the system is far beyond the phase transition points. The above numerical findings are validated by our theoretical analysis, which provides a general framework with important implications for Floquet engineering and information scrambling in chaotic systems.
We investigate both analytically and numerically the dynamics of quantum scrambling, characterized by out-of-time ordered correlators (OTOCs), in a non-Hermitian quantum kicked rotor subject to quantum resonance conditions. Analytical expressions for OTOCs as a function of time are obtained, demonstrating a sudden transition from linear growth to quadratic growth when the non-Hermitian parameter decays to zero. At this critical point, the rates of the linear growth are found to diverge to infinity, indicating the existence of quantum criticality at the boundary of the non-Hermitian regime. The underlying mechanism of this quantum criticality is uncovered, and possible applications in quantum metrology are discussed.
This paper reports the findings of the late time behavior of the out-of-time-ordered correlators (OTOCs) via quantum kicked rotor and kicked top models with PT-symmetric driving potential. An analytical expression of the OTOCs' power-law growth with time is yielded as $C(t)=G(K){t}^{\ensuremath{\gamma}}$, with $\ensuremath{\gamma}$ being system dependent. Interestingly, the growth rate G features a quantized response to the increase of the kick strength K. The physics behind this is the quantized absorption of energy from the non-Hermitian driving potential. This discovery and the ensuing establishment of the quantization mechanism in the dynamics of quantum chaos with non-Hermiticity will provide insights in chaotic dynamics, promising unprecedented observations in updated experiments.