Kicked rotator

The kicked rotator, also spelled as kicked rotor, is a prototype model for chaos and quantum chaos studies. It describes a particle that is constrained to move on a ring (equivalently: a rotating stick). The particle is kicked periodically by an homogeneous field (equivalently: the gravitation is switched on periodically in short pulses). The model is described by the Hamiltonian

Where ${\displaystyle \textstyle \delta }$ is the Dirac delta function, ${\displaystyle \textstyle x}$ is the angular position (for example, on a ring), taken modulo ${\displaystyle \textstyle 2\pi }$, ${\displaystyle \textstyle p}$ is the momentum, and ${\displaystyle \textstyle K}$ is the kicking strength. Its dynamics are described by the standard map

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