Physics Commons^™

Limits On Parameter Estimation Of Quantum Channels, Vishal Katariya

LSU Doctoral Dissertations

The aim of this thesis is to develop a theoretical framework to study parameter estimation of quantum channels. We begin by describing the classical task of parameter estimation that we build upon. In its most basic form, parameter estimation is the task of obtaining an estimate of an unknown parameter from some experimental data. This experimental data can be seen as a number of samples of a parameterized probability distribution. In general, the goal of such a task is to obtain an estimate of the unknown parameter while minimizing its error.

We study the task of estimating unknown parameters which …

An Introduction To Supersymmetric Quantum Mechanics, Vincent R. Siggia

Theses and Dissertations

In this thesis, the general framework of supersymmetric quantum mechanics and the path integral approach will be presented (as well as the worked out example of the supersymmetric harmonic oscillator). Then the theory will be specialized to the case of supersymmetric quantum mechanics on Riemannian manifolds, which will start from a supersymmetric Lagrangian for the general case and the special case for S2. Afterwards, there will be a discussion on the superfield formalism. Concluding this thesis will be the Hamiltonian formalism followed by the inclusion of deforma- tions by potentials.

The Classical Limit Of Entropic Quantum Dynamics, Anthony V. Demme

Physics

The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so that the center of mass (CM) of a system of N particles behaves as a classical particle. What is of interest is that ~ remains finite at all steps in the calculation and that the classical motion is obtained as the result of a central limit theorem. More explicitly we show that if the system is sufficiently large, and …

Combinatorial Algorithms For Perturbation Theory And Application On Quantum Computing, Yudong Cao

Open Access Dissertations

Quantum computing is an emerging area between computer science and physics. Numerous problems in quantum computing involve quantum many-body interactions. This dissertation concerns the problem of simulating arbitrary quantum many-body interactions using realistic two-body interactions. To address this issue, a general class of techniques called perturbative reductions (or perturbative gadgets) is adopted from quantum complexity theory and in this dissertation these techniques are improved for experimental considerations. The idea of perturbative reduction is based on the mathematical machinery of perturbation theory in quantum physics. A central theme of this dissertation is then to analyze the combinatorial structure of the perturbation …

Elements Of The Mathematical Formulation Of Quantum Mechanics, Keunjae Go

Senior Honors Papers / Undergraduate Theses

In this paper, we will explore some of the basic elements of the mathematical formulation of quantum mechanics. In the first section, I will list the motivations for introducing a probability model that is quite different from that of the classical probability theory, but still shares quite a few significant commonalities. Later in the paper, I will discuss the quantum probability theory in detail, while paying a brief attention to some of the axioms (by Birkhoff and von Neumann) that illustrate both the commonalities and differences between classical mechanics and quantum mechanics. This paper will end with a presentation of …

On Electromagnetic And Quantum Invisibility, Pattabhiraju Chowdary Mundru

Doctoral Dissertations

The principle objective of this dissertation is to investigate the fundamental properties of electromagnetic wave interactions with artificially fabricated materials i.e., metamaterials for application in advanced stealth technology called electromagnetic cloaking. The main goal is to theoretically design a metamaterial shell around an object that completely eliminates the dipolar and higher order multipolar scattering, thus making the object invisible.

In this context, we developed a quasi-effective medium theory that determines the optical properties of multi-layered-composites beyond the quasi-static limit. The proposed theory exactly reproduces the far-field scattering/extinction cross sections through an iterative process in which mode-dependent quasi-effective impedances of the …

Field Theoretic Lagrangian From Off-Shell Supermultiplet Gauge Quotients, Gregory Katona

Electronic Theses and Dissertations

Recent efforts to classify off-shell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a node-pair transformtion between fermionic bosonic component fields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge-quotients by supersymmetric images of other Adinkras, and the correlated building of field theoretic worldline Lagrangians to accommodate both classical and quantum venues. We find Ref [40], that such gauge quotients do not yield other stand alone or "proper" Adinkras as afore …

Laser-Atom Interactions: A Multiresolution Approach, Nicholas Eric Vence

Doctoral Dissertations

Isolated, attosecond laser pulses have allowed real-time measurement and control of electrons on atomic time scales. We present an explicit time-evolution scheme solving the time dependent Schro ̈dinger equation, which employs an adaptive, discontinuous, spectral-element basis that automatically refines to accommodate the requested precision providing efficient computation across many length scales in multiple dimensions. This method is illustrated through time evolution studies of single electron atoms and molecular ions in three and four dimensions under the influence of intense, few-cycle laser pulses.

Techniques To Characterize Vapor Cell Performance For A Nuclear-Magnetic-Resonance Gyroscope, James Julian Mirijanian

Master's Theses

Research was performed to improve the procedures for testing performance parameters of vapor cells for a nuclear-magnetic-resonance gyroscope. In addition to summarizing the theoretical infrastructure of the technology, this research resulted in the development and successful implementation of new techniques to characterize gyro cell performance.

One of the most important parameters to measure for gyro performance is the longitudinal spin lifetime of polarized xenon atoms in the vapor cell. The newly implemented technique for measuring these lifetimes matches results from the industry standard method to within 3.5% error while reducing the average testing time by 76% and increasing data resolution …

The Quantum Mechanics Of Supersymmetry, Joshua Gearhart

Physics

No abstract provided.

Holism And Non-Separability Applied To Quantum Mechanics, Catherine E. Nisson

Senior Honors Projects, 2010-2019

Einstein was never satisfied with quantum mechanics. He argued that quantum mechanics was incomplete for two main reasons; it violated the locality principle and the separability principle. The violation of separability is an unavoidable consequence of quantum interactions. Non-separability can be seen in quantum entanglement. Non-locality, however, is more controversial. Einstein and his associates published the EPR paper in order to argue for the incompleteness of quantum mechanics. Years later, John Bell formulated what became known as the Bell Inequalities in response to the EPR paper. The Bell Inequalities are seen as a major obstacle for quantum locality. I will …

On Relational Quantum Mechanics, Oscar Acosta

Open Access Theses & Dissertations

A problem facing quantum mechanics is that there are a number of views or interpretations available that purport to 'explain' quantum mechanics. In this paper I discuss and analyze the view of relational quantum mechanics by Carlo Rovelli in the context of theoretical underdetermination. I will show that even though Rovelli offers a view that consolidates some of the aspects of competing theories it still falls short of breaking out of the theoretical underdetermination. The criteria that I have used to consider a theory successful in this context is one that increases the predictive output of quantum theory. Lacking an …

The Problem Of Time In Quantum Mechanics, Crisol J. Escobedo

Open Access Theses & Dissertations

The purpose of my Thesis is to gain a better understanding of the nature of time and the problems associated with time. For example, I aim to explore the problem associated with the energy-time uncertainty relation due to the lack of a universal operator for time. Using Jan Hilgevoord's work, I will explore the idea that if a measure of time is to be obtained in quantum mechanics, then time has to be a property of physical systems that can only be measured in relation to other systems. As such, time cannot be independent of physical systems. This implies that …

Implementing Quantum Random Walks In Two-Dimensions With Application To Diffusion-Limited Aggregation, Colin Frederick Sanberg

Undergraduate Honors Thesis Collection

This study simulates random movement and aggregation of particles in two-dimensional space based upon both quantum and classical mechanics. Using an original computer program to perform the calculations, the objective is to compare how quantum effects influence the random movement of a particle in comparison to the classical random movement. These effects are further studied by analyzing how the amassing of particles around a "seed" is affected by the differences in the random movement. Using the classical models that were generated as the basis of comparison, the initial results show that the quantum model aggregate grows at a slower ratc …

Representations For Understanding The Stern-Gerlach Effect, Jared R. Stenson

Theses and Dissertations

The traditional explanation of the Stern-Gerlach effect carries with it several very subtle assumptions and approximations. We point out the degree to which this fact has affected the way we practice and interpret modern physics. In order to gain a more complete understanding of the Stern-Gerlach effect beyond the standard approximations and assumptions it typically carries, we introduce the inhomogeneous Stern-Gerlach effect in which the strong uniform field component is removed. This change allows us to easily identify precession as a critical concept. It also provides us with a means by which to study precession and analyze it critically. By …

Iteration Methods For Approximating The Lowest Order Energy Eigenstate Of A Given Symmetry For One- And Two-Dimensional Systems, Chad Everett Junkermeier

Theses and Dissertations

Using the idea that a quantum mechanical system drops to its ground state as its temperature goes to absolute zero several operators are devised to enable the approximation of the lowest order energy eigenstate of a given symmetry; as well as an approximation to the energy eigenvalue of the same order.