Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor Page: 3
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part of the de Broglie-Bohm quantum theory of motion is given, and applied to quantum Lyapunov
exponents for Bohmian trajectories.
Chapter 3 has a short introduction to the kicked rotor model. Its connection to a simple pendulum
and the modern realistic quantum model of the atom optics kicked rotor is given. The experimental
set-up of the atom optics kicked rotor, the theoretical derivation of the Hamiltonian from the real
model and the initial conditions are introduced. The classical map for the kicked rotor from the
Hamiltonian and Hamilton's equations is derived. The derivation of the map in quantum mechanics
is also presented.
Chapter 4 gives the new findings on the local Lyapunov exponent of the classical kicked rotor.
Trajectory simulation from a numerical approach and an analytical study of the upper bound of
the two adjacent trajectories are reported. The Lyapunov exponents as a function of the classical
control parameter K are computed based on Benettin et al. approach . Stability regions in the
chaotic sea are discovered numerically and analyzed.
Chapter 5 reports the study of momentum diffusion of the classical kicked rotor. Fifteen anoma-
lous diffusion regions are found for the control parameter K from 0 to 100. The numerical data
for momentum diffusion is well fitted by a power law D(K)NR(K) The corresponding exponents
3(K) and coefficients D(K) are obtained numerically. The relation of the regions to the classical
accelerator mode islands is studied.
Chapter 6 reports the chaos study on quantum kicked rotor. The map of Bohmian trajectories
is similar to the classical map at quantum resonance. It is derived first and then the Benettin et al.
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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/m1/20/: accessed June 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .