Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor Page: XII
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8.1 Momentum diffusion de Broglie-Bohm approach with an initial zero-momentum state.
The control parameter is K= 12.5. Subgraphs (a), (b), and (c) are for the nonreso-
nant case with k = 2, where the dash-dot lines are the classical (K2/2)N for refer-
ence. (a) The numerical data of a weighted average for (5)2 for time from 0 to 100
kicks. (b) The numerical data of a weighted average for twice the quantum potential
2Q for time from 0 to 100 kicks. (c) The sum of (a) and (b), which is a weighted
average for twice the quantum kinetic energy. (d) Resonant case with k = 4. The
dots are the numerical data, the dash-dot curve is (K2/2)N2 for reference, and the
solid line is a fitted quadratic curve. ......................85
B.1 Higher resolution on K for the Lyapunov exponent of the classical trajectories at
Benettin et al. approach. AK =0.002 (a) K= 7n region. Dashed line points to
K= 7n and solid lines illustrate region of Eq. (4.13) (b) K= 8n region. Solid lines il-
lustrate region of Eq. (4.12) while the dashed line is the right boundary of the second
accelerator mode islands (c) K= 9 region. Dashed line points to K= 9 and solid
lines illustrate region of Eq. (4.13) (d) K = 10 region. Solid lines illustrate region
of Eq. (4.12) and the dashed line is the right edge of the second accelerator mode
islands. ........................................ 103
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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/m1/14/: accessed December 13, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .