Paraphrase the following text using more academic and scientific language Use a neutral tone and avoid repetitions of words and phrases：When the noise strength $f_n$ is relatively small compared to th

When the magnitude of noise strength $f_n$ is relatively smaller than that of the kick strength $K$, it is feasible to use perturbation theory to expand the exponential term $e^{-ik_ncos^2\theta}$ in the Floquet operator $\hat{F}^{k_n}$. The expansion can be expressed as Eq. (1), where terms greater than $k^2_n$ are neglected. By substituting the expanded equation into Eq. (\ref{fkn}) and Eq. (\ref{asr}), and gathering terms with the same $k_n$ order, we obtain Eq. (2), where $A_r(N)$ is approximated, and $C_r$ represents a constant.