Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor Page: 48
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100, respectively. Only for this general profile we used the rather coarse resolution of 2000 values
of K evenly spaced between 0 and 100.
The solid curve in Fig. 5.1 is from Meiss, et al. ,
DL 1- 2j2 ( K) - J2 ( K) + 2J32 ( K)
K2/2 [1 +J2(K)]2 ' (5.6)
where Jn is a Bessel function of order n. It generally fits the numerical data well for the control
parameter K from 2 to 100, except for (almost) periodic large deviations due to accelerator modes.
This equation takes into account more correlation terms than the equation of Rechester and White
 and extends the fit to the data for down to K 2. Ichikawa, et al.  have made a careful
study of the region 0.9716 < K < 6.2832 and show that this formula fits the data qualitatively down
to K 1.8, but it does not take into account the resonances due to accelerator modes.
Rechester and White  in their Fig. 1, reproduced as Fig. 7.17 in Ott , show the momen-
tum diffusion from K= 0 to 50. They state on the basis of their Eq. (21) that in the limit of "large" K
the momentum diffusion ratio DL to K2/2 approaches unity. Equation (5.6) shows that for K= 95
the maximum linear diffusion ratio is about 18% greater than one. Even for K= 100, 000 the ratio
still deviates from unity by 0.5%. Figure 1 of Rechester and White  does not show the full extent
of resonances near the maxima. Oscillations about unity in the linear diffusion ratio were first found
by Chirikov .
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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/m1/65/: accessed May 26, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .