Dynamics of fluctuation correlation in a periodically driven classical system

Abstract

A many-body interacting system of classical kicked rotor serves as a prototypical model for studying Floquet heating dynamics. Having established the fact that this system exhibits a long-lived prethermal phase with quasi-conserved average Hamiltonian before entering into the chaotic heating regime, we use spatio-temporal fluctuation correlation of kinetic energy as a two-point observable to probe the above dynamic phases. We remarkably find the diffusive transport of fluctuation in the prethermal regime suggesting a novel underlying hydrodynamic picture in a generalized Gibbs ensemble with a definite temperature that depends on the driving parameter and the initial conditions. On the other hand, the heating regime is characterized by a diffusive growth of kinetic energy where the correlation is sharply localized around the fluctuation center for all time. Consequently, we attribute non-diffusive and non-localize structure of correlation to the crossover regime, connecting the prethermal phase to the heating phase, where the kinetic energy displays a complicated growth structure. We understand these numerical findings using the notion of relative phase matching where prethermal phase (heating regime) refers to an effectively coupled (isolated) nature of the rotors. We exploit the statistical uncorrelated nature of the angles of the rotors in the heating regime to find the analytical form of the correlator that mimics our numerical results in a convincing way.