Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor Page: 13
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H(p,x) 2M +Kcosx Y 8(t- nT) (3.2)
This model of the classical kicked rotor is also called the standard model and is one examples
of one-dimensional Hamiltonian chaos because it is time dependent.
The dimensionless form of the Hamiltonian is 
H(p, x) = - + Kcosx 8(t- n) (3.3)
The realistic model is shown in Fig. 3.1 (a). The simple pendulum has a force which is -mgsinx,
where x is the angle from the vertical, so the potential of the pendulum is -mgcosx. We now
assume that there is no gravity, but the pendulum is blown by a periodically varying 6- function
wind as illustrated by Fig. 3.1 (b). This is one example of pendulum kicked by a "8- kick force"
(Discussion with Dr. M. O. Scully).
3.2.3 Mapping of the Classical Kicked Rotor
The mapping of the standard model is as following 
Xn+ 1 = Xn + Pn+ 1 Pn+1 = Pn + Ksin(xn) (3.4)
The momentum is injected by the 8- kick with strength Ksin(xn) at time t= n and followed by
free evolution for a unit time, where the dimensionless time is in units of time per period.
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Zheng, Yindong. Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor, dissertation, August 2005; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc4824/m1/30/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .