Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor Page: 13
The following text was automatically extracted from the image on this page using optical character recognition software:
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.
Here’s what’s next.
This dissertation can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Dissertation.
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 September 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .