### On Chaos and Anomalous Diffusion in Classical and Quantum Mechanical Systems

**Date:**August 1998

**Creator:**Stefancich, Marco

**Description:**The phenomenon of dynamically induced anomalous diffusion is both the classical and quantum kicked rotor is investigated in this dissertation. We discuss the capability of the quantum mechanical version of the system to reproduce for extended periods the corresponding classical chaotic behavior.

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### 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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### Decoherence, Master Equation for Open Quantum Systems, and the Subordination Theory

**Date:**August 2005

**Creator:**Giraldi, Filippo

**Description:**This thesis addresses the problem of a form of anomalous decoherence that sheds light into the spectroscopy of blinking quantum dots. The system studied is a two-state system, interacting with an external environment that has the effect of establishing an interaction between the two states, via a coherence generating coupling, called inphasing. The collisions with the environment produce also decoherence, named dephasing. Decoherence is interpreted as the entanglement of the coherent superposition of these two states with the environment. The joint action of inphasing and dephasing generates a Markov master equation statistically equivalent to a random walker jumping from one state to the other. This model can be used to describe intermittent fluorescence, as a sequence of "light on" and "light off" states. The experiments on blinking quantum dots indicate that the sojourn times are distributed with an inverse power law. Thus, a proposal to turn the model for Poisson fluorescence intermittency into a model for non-Poisson fluorescence intermittency is made. The collision-like interaction of the two-state system with the environment is assumed to takes place at random times rather than at regular times. The time distance between one collision and the next is given by a distribution, called the ...

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### Estimation of Sparse Jacobian Matrices and Graph Coloring Problems

**Date:**June 1981

**Creator:**Coleman, Thomas F. & Moré, Jorge J.

**Description:**Given a mapping with a sparse Jacobian matrix, the problem of minimizing the number of function evaluations needed to estimate the Jacobian matrix by differences is investigated. This problem can be attacked as a graph coloring problem and this approach leads to very efficient algorithms. The behavior of these algorithms is studied and, in particular, it is proved that two of the algorithms are optimal for band graphs. Numerical evidence is presented which indicates that these two algorithms are nearly optimal on practical problems.

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### A Study of Quantum Electron Dynamics in Periodic Superlattices under Electric Fields

**Date:**May 1996

**Creator:**Yuan, Daiqing

**Description:**This thesis examines the quantum dynamics of electrons in periodic semiconductor superlattices in the presence of electric fields, especially uniform static fields. Chapter 1 is an introduction to this vast and active field of research, with an analysis and suggested solutions to the fundamental theoretical difficulties. Chapter 2 is a detailed historical review of relevant theories, and Chapter 3 is a historical review of experiments. Chapter 4 is devoted to the time-independent quantum mechanical study of the electric-field-induced changes in the transmission properties of ballistic electrons, using the transfer matrix method. In Chapter 5, a new time-dependent quantum mechanical model free from the fundamental theoretical difficulties is introduced, with its validity tested at various limiting cases. A simplified method for calculating field-free bands of various potential models is designed. In Chapter 6, the general features of "Shifting Periodicity", a distinctive feature of this new model, is discussed, and a "Bloch-Floquet Theorem" is rigorously proven. Numerical evidences for the existence of Wannier-Stark-Ladders are presented, and the conditions for its experimental observability is also discussed. In Chapter 7, an analytical solution is found for Bloch Oscillations and Wannier-Stark-Ladders at low electric fields. In Chapter 8, a new quantum mechanical interpretation for Bloch ...

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### The Behavioral Changes that can be Realized when Leaders are Exposed to the Theories and Metaphors Found in Quantum Physics.

**Date:**August 2009

**Creator:**Godfrey, David Wayne

**Description:**Many are beginning to see the promise that the quantum world has offered those who manage and lead organizations (Wheatley, 1992; Zohar, 1997). The Newtonian world is one in which all "things" are reduced to their smallest parts, separated, divided, and analyzed with predictability, with complete control being the ultimate goal. The quantum world is one of infinite possibilities, infinite fields of influence, and infinite relationships. The hallmark characteristics found in a manager who has been schooled in the quantum sciences are flexibility, responsiveness, synchronicity, serendipity, creativity, innovation, participation, and motivation. In a quantum organization there is the constant awareness of the whole system, but there is also diversity (wave or particle), which allows for self-organization that is based on the environment and its requirements. In the quantum world many paths lead from A to Z, and depending on the path chosen, numerous realities wait to unfold. It was the goal of this research to explore the changing of leader behaviors through exposure to the models and theories found in quantum physics. From a quantum perspective this behavior change is possible; the only question is the readiness, willingness, and ability of the leaders to allow their behaviors to be surfaced ...

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### Conference on Quantum-Mechanical Methods in Valence Theory

**Date:**1952

**Creator:**unknown

**Description:**Proceedings from the Conference on Quantum-Mechanical Methods in Valence Theory organized into six sections: Atomic and Molecular Problems, The Link with Chemical Valence Concepts, Intermolecular and Nonbonded Interatomic Forces, Transcending the Primitive Approximations, Mathematical Developments, and Integrals. Some papers include additional discussion from other participants. Table of contents starts on page iii.

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### The Classical Limit of Quantum Mechanics

**Date:**December 1977

**Creator:**Hefley, Velton Wade

**Description:**The Feynman path integral formulation of quantum mechanics is a path integral representation for a propagator or probability amplitude in going between two points in space-time. The wave function is expressed in terms of an integral equation from which the Schrodinger equation can be derived. On taking the limit h — 0, the method of stationary phase can be applied and Newton's second law of motion is obtained. Also, the condition the phase vanishes leads to the Hamilton - Jacobi equation. The secondary objective of this paper is to study ways of relating quantum mechanics and classical mechanics. The Ehrenfest theorem is applied to a particle in an electromagnetic field. Expressions are found which are the hermitian Lorentz force operator, the hermitian torque operator, and the hermitian power operator.

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