Dynamics of fluctuation correlation in periodically driven classical system

TL;DR

This paper investigates the dynamic phases of a classical kicked rotor system under periodic driving, revealing diffusive fluctuation transport in the prethermal phase and localized correlations during heating, with analytical modeling supporting numerical results.

Contribution

It introduces a spatio-temporal fluctuation correlation approach to distinguish dynamic phases in driven classical systems, providing analytical insights into correlation behaviors.

Findings

Diffusive transport of fluctuations in the prethermal phase.

Localization of correlations during the heating regime.

Analytical correlator form matches numerical simulations.

Abstract

Having established the fact that interacting classical kicked rotor systems exhibit long-lived prethermal phase with quasi-conserved average Hamiltonian before entering into chaotic heating regime, we use spatio-temporal fluctuation correlation of kinetic energy to probe the above dynamic phases. We remarkably find the diffusive transport of fluctuation in the prethermal regime reminding us the underlying hydrodynamic picture in a generalized Gibbs ensemble with a definite temperature that depends on the driving parameter and initial conditions. On the other hand, the heating regime, characterized by a diffusive growth of kinetic energy, can sharply localize the correlation at 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 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.