Figure 6: Time evolution of the energy density obtained from leading order equations subject to noise.
With multiplicative noise the system absorbs energy indefinitely even at leading order. The energy density grows with a powerlaw 
for late times for arbitrary system parameters. Depending on whether the noise is white, i.e., completely uncorrelated in time or colored, i.e., correlated in time, the growth is quadratic or linear, respectively. From that we deduce that correlations in time slow down heating in the system. The data is shown for driving frequency Ω = 2.3 and interaction strength u = 1.0. The strength of the white noise is γ = 2.0/Ω2 whereas for colored noise we have chosen σ = 2/Ω2 and τ = 20/Ω.
