Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor Page: 27
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x 104 a) Trajectory Simulation
0 200 400 600 800
c) Logrithm of Distance Ratio
0 200 400 600 800 1000
d) Local Lyapunov Exponent
Figure 4.1: Trajectory simulation and Lyapunov exponent in the chaotic regime with K= 10 as
a function of time N. (a) Simulation of two adjacent trajectories in coordinate space with initial
separation distance d(0)- 10-6 and xo 3. (b) Ratio d(N)/d(0) of distances in phase space as
a function of time N. (c) Logarithm of d(N)/d(0). (d) Corresponding local Lyapunov exponent L in
x 1010 b) Distance Ratio
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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/m1/44/: accessed June 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .