Chaos and subdiffusion in the infinite-range coupled quantum kicked rotors

TL;DR

This paper investigates the chaotic behavior and subdiffusive energy growth in an infinite-range coupled quantum kicked rotor system, revealing ergodicity, nonlinear dynamics, and localization effects through analytical and numerical methods.

Contribution

It introduces a mapping of the coupled quantum kicked rotors to an interacting bosonic model and analyzes chaos, energy dynamics, and localization phenomena in this framework.

Findings

Energy increases as a power law with exponent ~2/3.

System tends to ergodicity in the large-size limit.

Lyapunov exponent decreases to zero in certain phase space regions.

Abstract

We map the infinite-range coupled quantum kicked rotors over an infinite-range coupled interacting bosonic model. In this way we can apply exact diagonalization up to quite large system sizes and confirm that the system tends to ergodicity in the large-size limit. In the thermodynamic limit the system is described by a set of coupled Gross-Pitaevskij equations equivalent to an effective nonlinear single-rotor Hamiltonian. These equations give rise to a power-law increase in time of the energy with exponent $\gamma\sim 2/3$ in a wide range of parameters. We explain this finding by means of a master-equation approach based on the noisy behaviour of the effective nonlinear single-rotor Hamiltonian and on the Anderson localization of the single-rotor Floquet states. Furthermore, we study chaos by means of the largest Lyapunov exponent and find that it decreases towards zero for portions of the phase space with increasing momentum. Finally, we show that some stroboscopic Floquet integrals of motion of the noninteracting dynamics deviate from their initial values over a time scale related to the interaction strength according to the Nekhoroshev theorem.