Derivation and Analysis of the Classical Motion Equation for a Modified Kicked Rotor Model

The classical motion equation for the proposed model can be derived through integration of the canonical equation. This integration yields the following evolution equation:

\begin{eqnarray} p_{n+1} &=& p_{n}+Ksin{2\theta_{n}},
\theta_{n+1} &=& \theta_{n}+p_{n+1}, \end{eqnarray}

It is noteworthy that the force term within the equation incorporates a factor of 2 in relation to the angle variable \theta_{n} when compared to the original kicked rotor model. This modification, however, does not result in substantial alterations to the classical evolution, provided the angle variable is appropriately rescaled. Consequently, the classical motion of the present model can be analyzed using methods analogous to those employed for the original kicked rotor model.