Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor

Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor

Date: August 2005
Creator: Zheng, Yindong
Description: The de Broglie-Bohm (BB) approach to quantum mechanics gives trajectories similar to classical trajectories except that they are also determined by a quantum potential. The quantum potential is a "fictitious potential" in the sense that it is part of the quantum kinetic energy. We use quantum trajectories to treat quantum chaos in a manner similar to classical chaos. For the kicked rotor, which is a bounded system, we use the Benettin et al. method to calculate both classical and quantum Lyapunov exponents as a function of control parameter K and find chaos in both cases. Within the chaotic sea we find in both cases nonchaotic stability regions for K equal to multiples of π. For even multiples of π the stability regions are associated with classical accelerator mode islands and for odd multiples of π they are associated with new oscillator modes. We examine the structure of these regions. Momentum diffusion of the quantum kicked rotor is studied with both BB and standard quantum mechanics (SQM). A general analytical expression is given for the momentum diffusion at quantum resonance of both BB and SQM. We obtain agreement between the two approaches in numerical experiments. For the case of nonresonance the ...
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Numerical Investigations of Quantum Effects of Chaos

Numerical Investigations of Quantum Effects of Chaos

Date: August 1993
Creator: Miroslaw, Latka
Description: The quantum dynamics of minimum uncertainty wave packets in a system described by the surface-state-electron (SSE) Hamiltonian are studied herein.
Contributing Partner: UNT Libraries
Studies of Classically Chaotic Quantum Systems within the Pseudo-Probablilty Formalism

Studies of Classically Chaotic Quantum Systems within the Pseudo-Probablilty Formalism

Date: August 1992
Creator: Roncaglia, Roberto
Description: The evolution of classically chaotic quantum systems is analyzed within the formalism of Quantum Pseudo-Probability Distributions. Due to the deep connections that a quantum system shows with its classical correspondent in this representation, the Pseudo-Probability formalism appears to be a useful method of investigation in the field of "Quantum Chaos." In the first part of the thesis we generalize this formalism to quantum systems containing spin operators. It is shown that a classical-like equation of motion for the pseudo-probability distribution ρw can be constructed, dρw/dt = (L_CL + L_QGD)ρw, which is rigorously equivalent to the quantum von Neumann-Liouville equation. The operator L_CL is undistinguishable from the classical operator that generates the semiclassical equations of motion. In the case of the spin-boson system this operator produces semiclassical chaos and is responsible for quantum irreversibility and the fast growth of quantum uncertainty. Carrying out explicit calculations for a spin-boson Hamiltonian the joint action of L_CL and L_QGD is illustrated. It is shown that the latter operator, L_QGD makes the spin system 'remember' its quantum nature, and competes with the irreversibility induced by the former operator. In the second part we test the idea of the enhancement of the quantum uncertainty triggered by ...
Contributing Partner: UNT Libraries