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arXiv:2604.13382 · Physical review. B./Physical review. B

Dynamics of wavepackets and entanglement in many-body kicked rotors under quantum resonance

Yangshuo Zhou, Jiao Wang

quant-phcond-mat.othernlin.CDnlin.SISubmitted Apr 15, 2026• Announced Apr 16, 2026• 0 citations
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Abstract

We investigate a many-body interacting system of quantum kicked rotors, where each rotor resides in its respective quantum resonance. Rich many-body dynamics are found to emerge from the interplay between the principal and secondary resonances. In particular, for both the wavepacket and bipartite entanglement entropy, we analytically demonstrate three distinct dynamical regimes -- quadratic spreading (growth), period-2 oscillation, and their hybrid -- governed by the respective symmetries of the relevant potentials. Based on these symmetries, the connection between the wavepacket and the entanglement dynamics is illustrated. Other related issues are also discussed, including higher-order resonance effects, the robustness of the predicted dynamical behaviors, extension to many-body kicked tops, and relevance to experimental studies.

Journal reference
Physical Review B 113, 144307 (2026)
DOI
10.1103/1lj8-xjps
Comments
17 pages, 7 figures

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We investigate a many-body interacting system of quantum kicked rotors, where each rotor resides in its respective quantum resonance. Rich many-body dynamics are found to emerge from the interplay between the principal and secondary resonances. In particular, for both the wavepacket and bipartite entanglement entropy, we analytically demonstrate three distinct dynamical regimes -- quadratic spreading (growth), period-2 oscillation, and their hybrid -- governed by the respective symmetries of the relevant potentials. Based on these symmetries, the connection between the wavepacket and the entanglement dynamics is illustrated. Other related issues are also discussed, including higher-order resonance effects, the robustness of the predicted dynamical behaviors, extension to many-body kicked tops, and relevance to experimental studies.
Quantum resonance in the paradigmatic kicked rotor system is a purely quantum effect that ignores the state of underlying classical chaos. In this work, it is shown that quantum resonance leads to superlinear entanglement production. In NNN interacting kicked rotors set to be at quantum resonance, entanglement growth is superlinear until a crossover timescale t∗{t}^{*}t∗, beyond which growth slows down to a logarithmic form with superimposed oscillations. By mapping positional interaction to momentum space and analytically assessing the linear entropy, we unravel the mechanism driving these two distinct growth profiles. The analytical result obtained for the linear entropy agrees with the corresponding numerical simulations performed for two and three interacting kicked rotors. The late time entanglement oscillation is sensitive to changes in scaled Planck's constant with a high-quality factor suitable for high-precision measurements. These results are amenable to an experimental realization on atom optics setups.
The kicked rotor and the kicked top are two paradigms of quantum chaos. The notions of quantum resonance and the pseudoclassical limit, developed in the study of the kicked rotor, have revealed an intriguing and unconventional aspect of classical-quantum correspondence. Here, we show that, by extending these notions to the kicked top, its rich dynamical behavior can be appreciated more thoroughly; of special interest is the entanglement entropy. In particular, the periodic synchronization between systems subject to different kicking strength can be conveniently understood and elaborated from the pseudoclassical perspective. The applicability of the suggested general pseudoclassical theory to the kicked rotor is also discussed.
The kicked rotor provides a simple yet powerful model for introducing many of the central concepts of classical and quantum chaos. Despite its apparent simplicity, it exhibits rich dynamical behavior and has found applications across a wide range of fields, including atomic and optical physics, condensed matter physics, and emerging quantum technologies. This chapter begins by exploring foundational ideas using the kicked rotor as a unifying framework. We first discuss the transition from regular to chaotic motion in the classical system, and then introduce key quantum phenomena such as dynamical localization and quantum resonances. Special attention is devoted to the emergence of characteristic time scales and their role in the quantum-classical correspondence. To make these ideas more concrete, we also provide a brief overview of experimental realizations of the kicked rotor and its variants, illustrating how theoretical concepts are implemented in practice. In the second part of the chapter, we guide the reader toward more recent and advanced developments. Topics include near-resonant dynamics, topological features of kicked systems, the emergence of quantum dynamical phases inferred from classical transport properties, and extensions to non-Hermitian physics. We conclude with a discussion of open problems and future perspectives, outlining directions in which the kicked rotor continues to offer valuable insights.
Despite the periodic kicks, a linear kicked rotor (LKR) is an integrable and exactly solvable model in which the kinetic energy term is linear in momentum. It was recently shown that spatially interacting LKRs are also integrable, and results in dynamical localization in the corresponding quantum regime. Similar localized phases exist in other nonintegrable models such as the coupled relativistic kicked rotors. This work, using a two-body LKR, demonstrates two main results; first, it is shown that chaos can be induced in the integrable linear kicked rotor through interactions between the momenta of rotors. An analytical estimate of its Lyapunov exponent is obtained. Second, the quantum dynamics of this chaotic model, upon variation of kicking and interaction strengths, is shown to exhibit a variety of phases: classically induced localization, dynamical localization, subdiffusive, and diffusive phases. We point out the signatures of these phases from the perspective of entanglement production in this system. By defining an effective Hilbert space dimension, the entanglement growth rate can be understood using appropriate random matrix averages.
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.