Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor Page: 70
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QUANTUM MOMENTUM DIFFUSION OF THE KICKED ROTOR:
STANDARD QUANTUM MECHANICAL APPROACH
Using standard quantum mechanics, we obtain the general solution for momentum diffusion at
quantum resonance. The analytical and numerical solutions both agree. For nonresonance the
numerical simulation of standard quantum mechanics gives a momentum diffusion that saturates,
which agrees with experimental results of the atom optics kicked rotor.
Since the first experimental atom optics realization of the quantum kicked rotor, the study of
momentum diffusion has been especially important [18, 20, 24, 33, 34, 35, 38]. With atom optics
kicked rotor, Peres's [62, 63] proposal of quantum chaos from perturbation on the potential can
be arranged experimentally [4, 64]. The study of quantum accelerator modes  and quantum
resonance [27, 66] can also be undertaken experimentally. In this chapter we study momentum
diffusion of the quantum kicked rotor using numerical simulation, which is necessary to go beyond
limited analytical solutions. Numerical diffusion rates are computed using a least squares fit to the
numerical data. For all the calculations our own implemented programs in Matlab  are used.
The solution of the Schrodinger equation solved in Chapter 6 for the kicked rotor in the form
of an expansion in momentum eigenstates is used, which is especially convenient to calculate
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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/m1/87/: accessed December 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .