  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.
