ASU Electronic Theses and Dissertations
This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.
In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.
Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.
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- All Subjects: Mathematics
- Creators: Suslov, Sergei K
- Creators: Yang, Yezhou
Description
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2011
Description
The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schr¨odinger equation for the simple harmonic oscillator in one dimension is constructed. Probability distributions of the particle linear position and momentum, are emphasized with Mathematica animations. The eigenfunctions qualitatively differ from the traditional standing waves of the one-dimensional Schrodinger equation. The physical relevance of these dynamic states is still questionable, and in order to investigate their physical meaning, animations could also be created for the squeezed coherent states. This will be addressed in future work.
ContributorsLopez, Raquel (Author) / Suslov, Sergei K (Thesis advisor) / Radunskaya, Ami (Committee member) / Castillo-Chavez, Carlos (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2012
Description
Currently, one of the biggest limiting factors for long-term deployment of autonomous systems is the power constraints of a platform. In particular, for aerial robots such as unmanned aerial vehicles (UAVs), the energy resource is the main driver of mission planning and operation definitions, as everything revolved around flight time. The focus of this work is to develop a new method of energy storage and charging for autonomous UAV systems, for use during long-term deployments in a constrained environment. We developed a charging solution that allows pre-equipped UAV system to land on top of designated charging pads and rapidly replenish their battery reserves, using a contact charging point. This system is designed to work with all types of rechargeable batteries, focusing on Lithium Polymer (LiPo) packs, that incorporate a battery management system for increased reliability. The project also explores optimization methods for fleets of UAV systems, to increase charging efficiency and extend battery lifespans. Each component of this project was first designed and tested in computer simulation. Following positive feedback and results, prototypes for each part of this system were developed and rigorously tested. Results show that the contact charging method is able to charge LiPo batteries at a 1-C rate, which is the industry standard rate, maintaining the same safety and efficiency standards as modern day direct connection chargers. Control software for these base stations was also created, to be integrated with a fleet management system, and optimizes UAV charge levels and distribution to extend LiPo battery lifetimes while still meeting expected mission demand. Each component of this project (hardware/software) was designed for manufacturing and implementation using industry standard tools, making it ideal for large-scale implementations. This system has been successfully tested with a fleet of UAV systems at Arizona State University, and is currently being integrated into an Arizona smart city environment for deployment.
ContributorsMian, Sami (Author) / Panchanathan, Sethuraman (Thesis advisor) / Berman, Spring (Committee member) / Yang, Yezhou (Committee member) / McDaniel, Troy (Committee member) / Arizona State University (Publisher)
Created2018
Description
Compressive sensing theory allows to sense and reconstruct signals/images with lower sampling rate than Nyquist rate. Applications in resource constrained environment stand to benefit from this theory, opening up many possibilities for new applications at the same time. The traditional inference pipeline for computer vision sequence reconstructing the image from compressive measurements. However,the reconstruction process is a computationally expensive step that also provides poor results at high compression rate. There have been several successful attempts to perform inference tasks directly on compressive measurements such as activity recognition. In this thesis, I am interested to tackle a more challenging vision problem - Visual question answering (VQA) without reconstructing the compressive images. I investigate the feasibility of this problem with a series of experiments, and I evaluate proposed methods on a VQA dataset and discuss promising results and direction for future work.
ContributorsHuang, Li-Chin (Author) / Turaga, Pavan (Thesis advisor) / Yang, Yezhou (Committee member) / Li, Baoxin (Committee member) / Arizona State University (Publisher)
Created2017