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Articles 1 - 19 of 19
Full-Text Articles in Physical Sciences and Mathematics
Representation Theory And Its Applications In Physics, Max Varverakis
Representation Theory And Its Applications In Physics, Max Varverakis
Master's Theses
Representation theory, which encodes the elements of a group as linear operators on a vector space, has far-reaching implications in physics. Fundamental results in quantum physics emerge directly from the representations describing physical symmetries. We first examine the connections between specific representations and the principles of quantum mechanics. Then, we shift our focus to the braid group, which describes the algebraic structure of braids. We apply representations of the braid group to physical systems in order to investigate quasiparticles known as anyons. Finally, we obtain governing equations of anyonic systems to highlight the differences between braiding statistics and conventional Bose-Einstein/Fermi-Dirac …
The Future Between Quantum Computing And Cybersecurity, Daniel Dorazio
The Future Between Quantum Computing And Cybersecurity, Daniel Dorazio
Williams Honors College, Honors Research Projects
Quantum computing, a novel branch of technology based on quantum theory, processes information in ways beyond the capabilities of classical computers. Traditional computers use binary digits [bits], but quantum computers use quantum binary digits [qubits] that can exist in multiple states simultaneously. Since developing the first two-qubit quantum computer in 1998, the quantum computing field has experienced rapid growth.
Cryptographic algorithms such as RSA and ECC, essential for internet security, rely on the difficulty of complex math problems that classical computers can’t solve. However, the advancement of quantum technology threatens these encryption systems. Algorithms, such as Shor’s, leverage the power …
Overcoming Atmospheric Effects In Quantum Cryptography, Brian Joseph Rollick
Overcoming Atmospheric Effects In Quantum Cryptography, Brian Joseph Rollick
Doctoral Dissertations
Quantum Computers will have the potential to greatly assist us in problems such as searching, optimization and even drug discovery. Unfortunately, among these newfound capabilities is one which allows one to break RSA encryption in orders of magnitude less time. One promising countermeasure to secure our communication today and in the future is the one time pad, although it is very difficult to generate and distribute. Quantum Key Distribution offers a practical method for two authenticated parties to generate a key. Whereby the parties, Alice and Bob, share quantum states and use physical laws to place an upper bound on …
Circulation Transfer Between Adjacent Target Bose-Einstein Condensates, Charles B. Henry
Circulation Transfer Between Adjacent Target Bose-Einstein Condensates, Charles B. Henry
Honors College Theses
We propose an atomtronic rotation sensor design that consists of an array of Bose-Einstein Condensates (BECs) that are confined in a double-target-array potential. The rotation sensor's purpose is to measure the speed of the rotating frame, with respect to the “fixed stars", the sensor rests in. The atomtronic system is an ultracold gas of sodium atoms that have been compressed by laser light into a thin quasi-2D horizontal plane and further confined in the horizontal plane by a double-target-array potential. A target BEC is a combination of disk BEC that is surrounded by a ring BEC. A double-target BEC is …
Solving Chromatic Number With Quantum Search And Quantum Counting, David Lutze
Solving Chromatic Number With Quantum Search And Quantum Counting, David Lutze
Master's Theses
This thesis presents a novel quantum algorithm that solves the Chromatic Number problem. Complexity analysis of this algorithm revealed a run time of O(2n/2n2(log2n)2). This is an improvement over the best known algorithm, with a run time of 2nnO(1) [1]. This algorithm uses the Quantum Search algorithm (often called Grover's Algorithm), and the Quantum Counting algorithm. Chromatic Number is an example of an NP-Hard problem, which suggests that other NP-Hard problems can also benefit from a speed-up provided by quantum technology. This has wide implications as many real world problems can …
Optomechanical Quantum Entanglement, Kahlil Y. Dixon
Optomechanical Quantum Entanglement, Kahlil Y. Dixon
LSU Doctoral Dissertations
As classical technology approaches its limits, exploration of quantum technologies is critical. Quantum optics will be the basis of various cutting-edge research and applications in quantum technology. In particular, quantum optics quite efficacious when applied to quantum networks and the quantum internet. Quantum Optomechanics, a subfield of quantum optics, contains some novel methods for entanglement generation. These entanglement production methods exploit the noise re-encoding process, which is most often associated with creating unwanted phase noise in optical circuits. Using the adapted two-photon formalism and experimental results, we simulate (in an experimentally viable parameter space) optomechanical entanglement generation experiments. These simulations …
Quantum Optics, Entanglement, And Bell's Theorem, Andrew D. Poverman
Quantum Optics, Entanglement, And Bell's Theorem, Andrew D. Poverman
Senior Projects Spring 2021
The field of quantum optics provides a wonderful setting in which to study fundamental aspects of quantum mechanics such as entanglement, Bell's theorem, and non-locality. This thesis presents theoretical discussions of qubits, entanglement, and Bell's theorem in addition to experimental discussions on the nature of photons, creating entangled states using Spontaneous Parametric Down-Conversion (SPDC), and a Bell Test with polarization entangled photons. The experimental sections are written to be useful as instructions for one to conduct these experiments on their own. By doing these experiments, one will gain familiarity with quantum optics experiments as well as a firmer grasp on …
Qwasi: The Quantum Walk Simulator, Warren V. Wilson
Qwasi: The Quantum Walk Simulator, Warren V. Wilson
Theses and Dissertations
As quantum computing continues to evolve, the ability to design and analyze novel quantum algorithms becomes a necessary focus for research. In many instances, the virtues of quantum algorithms only become evident when compared to their classical counterparts, so a study of the former often begins with a consideration of the latter. This is very much the case with quantum walk algorithms, as the success of random walks and their many, varied applications have inspired much interest in quantum correlates. Unfortunately, finding purely algebraic solutions for quantum walks is an elusive endeavor. At best, and when solvable, they require simple …
On Characterizing Quantum Processes And Detectors, Kevin Valson Jacob
On Characterizing Quantum Processes And Detectors, Kevin Valson Jacob
LSU Doctoral Dissertations
In 2009, physicists at the National Institute of Standards and Technology in Colorado, Boulder developed what could arguable be called the first rudimentary quantum computer [1]. The past decade has seen unprecedented improvements in quantum information science culminating in the demonstration of quantum supremacy --- that quantum computers can solve problems that are impractical to be solved on the best supercomputers [2]. This remarkable progress necessitates the development of techniques to characterize the quantum devices that are being developed. In my thesis, I will focus on such devices that manipulate and detect light.
In Chapter 1, I will introduce the …
An Introduction To Supersymmetric Quantum Mechanics, Vincent R. Siggia
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.
Quantum Entanglement Of One-Dimensional Spinless Fermions, Emanuel Casiano-Diaz
Quantum Entanglement Of One-Dimensional Spinless Fermions, Emanuel Casiano-Diaz
Graduate College Dissertations and Theses
The constituents of a quantum many-body system can be inextricably linked, a phenomenon known as quantum entanglement. Entanglement can be used as a resource for quantum computing, quantum communication and detecting phase transitions, among others. The amount of entanglement can be quantified via the von Neumann and Rényi entropies, which have their origins in information theory.
In this work, the quantum entanglement between subsystems of a one dimen- sional lattice model of fermions is quantified. The von Neumann and Rényi entropies were calculated for two types of subsystems. In the first study, the subsystems were treated as two subsets of …
The Entropic Dynamics Approach To The Paradigmatic Quantum Mechanical Phenomena, Susan Difranzo
The Entropic Dynamics Approach To The Paradigmatic Quantum Mechanical Phenomena, Susan Difranzo
Legacy Theses & Dissertations (2009 - 2024)
Standard Quantum Mechanics, although successful in terms of calculating and predicting
Simulation Of Nuclear Fusion Using A One Dimensional Particle In Cell Method, Steven T. Margell
Simulation Of Nuclear Fusion Using A One Dimensional Particle In Cell Method, Steven T. Margell
Cal Poly Humboldt theses and projects
In this thesis several novel techniques are developed to simulate fusion events in an isotropic, electrostatic three-dimensional Deuterium-Tritium plasma. These techniques allow us to accurately predict three-dimensional collision events with a one-dimensional model while simultaneously reducing compute time via a nearest neighbor algorithm. Furthermore, a fusion model based on first principles is developed that yields an average fusion reactivity which correlates well with empirical results.
Photovoltaics: An Investigation Into The Origins Of Efficiency On All Scales, Jeremy Alexander Bannister
Photovoltaics: An Investigation Into The Origins Of Efficiency On All Scales, Jeremy Alexander Bannister
Senior Projects Spring 2016
This project is comprised of a set of parallel investigations, which share the common mo- tivation of increasing the efficiency of photovoltaics. First, the reader is introduced to core concepts of photovoltaic energy conversion via a semi-classical description of the phys- ical system. Second, a key player in photovoltaic efficiency calculations, the exciton, is discussed in greater quantum mechanical detail. The reader will be taken through a nu- merical derivation of the low-energy exciton states in various geometries, including a line segment, a circle and a sphere. These numerical calculations are done using Mathematica, a computer program which, due to …
Nonlocal Polarization Interferometry And Entanglement Detection, Brian P. Williams
Nonlocal Polarization Interferometry And Entanglement Detection, Brian P. Williams
Doctoral Dissertations
At present, quantum entanglement is a resource, distributed to enable a variety of quantum information applications such as quantum key distribution, superdense coding, and teleportation. Necessarily, the distribution and characterization of entanglement is fundamental to its application. This dissertation details three research efforts to enable nonlocal entanglement detection, distribution, and characterization. Foremost of these efforts, we present the theory and demonstration of a nonlocal polarization interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer’s unique correlation dependence on the anti-diagonal elements of the density matrix, which have distinct bounds for separable states …
Isotropic Oscillator Under A Magnetic And Spatially Varying Electric Field, David L. Frost Mr., Frank Hagelberg
Isotropic Oscillator Under A Magnetic And Spatially Varying Electric Field, David L. Frost Mr., Frank Hagelberg
Undergraduate Honors Theses
We investigate the energy levels of a particle confined in the isotropic oscillator potential with a magnetic and spatially varying electric field. Here we are able to exactly solve the Schrodinger equation, using matrix methods, for the first excited states. To this end we find that the spatial gradient of the electric field acts as a magnetic field in certain circumstances. Here we present the changes in the energy levels as functions of the electric field, and other parameters.
Controllability Of Open Quantum Optical Systems: Photon Fock States In A Cavity, Byron Henry Lowry
Controllability Of Open Quantum Optical Systems: Photon Fock States In A Cavity, Byron Henry Lowry
Doctoral Dissertations and Master's Theses
There has always been a significant interest in using optical systems to control quantum phenomena. A major barrier to controllability of quantum optical systems is the fact that the systems are usually innite dimensional open systems, two cases which have mostly negative controllability results. This thesis develops three new definitions of controllability and reformulates a previous controllability theorem in order to apply the theorem to the system of interest. Then, the controllability of a pumped dissipative quantum optical cavity with engineered decoherence is investigated using previously developed concepts in quantum control theory, as well as the ones developed in this …
Hilbert Space Theory And Applications In Basic Quantum Mechanics, Matthew Gagne
Hilbert Space Theory And Applications In Basic Quantum Mechanics, Matthew Gagne
Mathematics
We explore the basic mathematical physics of quantum mechanics. Our primary focus will be on Hilbert space theory and applications as well as the theory of linear operators on Hilbert space. We show how Hermitian operators are used to represent quantum observables and investigate the spectrum of various linear operators. We discuss deviation and uncertainty and briefly suggest how symmetry and representations are involved in quantum theory.
Parsimony And Quantum Mechanics: An Analysis Of The Copenhagen And Bohmian Interpretations, Jhenna Voorhis
Parsimony And Quantum Mechanics: An Analysis Of The Copenhagen And Bohmian Interpretations, Jhenna Voorhis
Scripps Senior Theses
Parsimony, sometime referred to as simplicity, is an effective criterion of theory choice in the case of Quantum Mechanics. The Copenhagen and Bohmian interpretations are rival theories, with the Bohmian interpretation being more parsimonious. More parsimonious theories have a higher probability of being true than less parsimonious rivals. The Bohmian interpretation should thus be preferred on these grounds.