Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor Page: 54
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K1 corresponding to the maximum diffusion in that region of anomalous momentum diffusion. The
third row gives the difference in control parameters between adjacent resonances K1 -K1_1. These
differences deviate from 27t by +2.% or less. The fourth row gives the range of the nonlinear region,
which is in good agreement with Eq. (5.8), and the fifth row gives the width of the region. The sixth
and seventh rows gives the values of (3 = 3(K) and D1 = D(K) for the values of the exponent and
the coefficient, respectively, in Eq. (5.7) at the value of the control parameter K corresponding to
the maximum momentum diffusion in accelerator mode region 1. Finally, row eight gives the percent
fitting error of Eq. (5.7) to the numerical data.
Figures 5.4 (a) and (b) are plots of the momentum diffusion vs. the time N in kicks for three
values of K in the region near K and near Ks, respectively. All the curves show nonlinear behavior.
The least square fit of Eq. (5.7) to the numerical data in the asymptotic region from N= 1000 to
5000 kicks is shown for each case. The fitted curves are inside the numerical data curves.
5.5 Linear Momentum Diffusion
Figure 5.5 shows the numerical data for the momentum diffusion ((Ap)2) for the control pa-
rameter K= 10 in the linear region as a function of time (or kicks) from N= 1 to 5000 kicks.
The solid line is the least squares fit of DLN to the numerical data for the momentum diffusion
(Ap)2) for Nfrom 1 to 5000. The value obtained for the linear diffusion rate DL = 32.92 deviates
from the numerical data by an average of 0.32%. The momentum diffusion without correlations
K(Ap)2o = (K2/2)Nis shown as the dashed line. The value of K2/2 deviates from DL by 51.9%.
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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/m1/71/: accessed October 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .