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
I
{\displaystyle I}
) in an inhomogeneous "gravitation like" field that is periodically switched on in short pulses. The model is described by the Hamiltonian
H
(
θ
,
p
θ
,
t
)
=
p
θ
2
2
I
+
K
cos
θ
∑
n
=
−
∞
∞
δ
(
t
T
−
n
)
{\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
θ
∈
[
0
,
2
π
]
{\displaystyle \theta \in [0,2\pi ]}
is the angular position of the stick (
θ
=
π
{\displaystyle \theta =\pi }
corresponds to the position of the rotator at rest),
p
θ
{\displaystyle p_{\theta }}
is the conjugated momentum of
θ
{\displaystyle \theta }
,
K
{\displaystyle \textstyle K}
is the kicking strength,
T
{\displaystyle T}
is the kicking period and
δ
{\displaystyle \textstyle \delta }
is the Dirac delta function.
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