Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor Page: 75
The following text was automatically extracted from the image on this page using optical character recognition software:
Figure 7.1 (b) shows the momentum diffusion for nonresonance with k = 2. The dash-dot line
is the classical linear momentum diffusion (K2/2)N, which serves as a reference. The dots are
the numerical experimental data which is linear between 0 and about 28 kicks, and then begins to
saturate. Figure 7.1 (d) shows the momentum diffusion for resonance with k = 4. The dash-dot
line is the momentum diffusion for an initial plane wave (K2/2)N2 in Eq. (7.3). The dots are the
numerical simulation data that shows quadratic growth with a quadratic diffusion rate close to K2/2.
A least squares fit to the numerical data gives a quadratic diffusion rate of D= 76.2, which differs
from the analytical diffusion rate of K2/2 by 2.4% as shown in Table 7.1.
Figure 7.2 gives the results of momentum distribution and momentum diffusion using the ini-
tial Gaussian momentum distribution in Eq. (7.4) with a control parameter K= 12.5 for both the
resonant and nonresonant cases. The initial Gaussian momentum distribution describes the atom
optics kicked rotor more closely than the initial zero momentum state .
Figure 7.2 (a) shows the momentum distribution as a function of time from 0 to 100 kicks for
the nonresonant case with k = 2. Figure 7.2 (c) shows the momentum distribution as a function
of time from 0 to 100 kicks for the resonant case with k = 4. Both distributions have an expected
symmetry around zero momentum. The probability distributions are similar to Fig. 7.1 (a) and (c).
Figure 7.2 (b) for the nonresonant case with k = 2 shows saturation after about 10 kicks, and
is similar to the experimental data for the atom optics kicked rotor . Figure 7.2 (d) shows the
momentum diffusion for the resonant case with k = 4, which is quadratic in kicks (time). For
K= 12.5 the theoretical momentum diffusion in Eq. (7.5) gives a rate D= 67.5, while the numerical
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/m1/92/: accessed October 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .