Kicked rotator

The kicked rotator, also spelled as kicked rotor, is a paradigmatic model for both Hamiltonian chaos (the study of chaos in Hamiltonian systems) and quantum chaos. It describes a free rotating stick (with moment of inertia ${\displaystyle I}$) in an inhomogeneous "gravitation like" field that is periodically switched on in short pulses. The model is described by the Hamiltonian

${\displaystyle {\mathcal {H}}(\theta ,p_{\theta },t)={\frac {p_{\theta }^{2}}{2I}}+K\cos \theta \sum _{n=-\infty }^{\infty }\delta \left({\frac {t}{T}}-n\right)}$,

where ${\displaystyle \theta \in [0,2\pi ]}$ is the angular position of the stick (${\displaystyle \theta =\pi }$ corresponds to the position of the rotator at rest), ${\displaystyle p_{\theta }}$ is the conjugated momentum of ${\displaystyle \theta }$, ${\displaystyle \textstyle K}$ is the kicking strength, ${\displaystyle T}$ is the kicking period and ${\displaystyle \textstyle \delta }$ is the Dirac delta function.