Quantum Physics Commons^™

Basics Of Factorization In A Scalar Yukawa Field Theory, F. Aslan, L. Gamberg, J.O. Gonzalez-Hernandez, T. Rainaldi, T. C. Rogers

Physics Faculty Publications

The factorization theorems of QCD apply equally well to most simple quantum field theories that require renormalization but where direct calculations are much more straightforward. Working with these simpler theories is convenient for stress testing the limits of the factorization program and for examining general properties of the parton density functions or other correlation functions that might be necessary for a factorized description of a process. With this view in mind, we review the steps of factorization in a real scalar Yukawa field theory for both deep inelastic scattering and semi-inclusive deep inelastic scattering cross sections. In the case of …

Perspectives On Determinism In Quantum Mechanics: Born, Bohm, And The “Quantal Newtonian” Laws, Viraht Sahni

Publications and Research

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen–Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a “probability amplitude.” A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper, we present a new perspective on such determinism. The ideas are based on the equations of motion or “Quantal Newtonian” Laws obeyed by each electron. These Laws, derived from …

Golay Codes And Quantum Contextuality, Mordecai Waegell, P. K. Aravind

Mathematics, Physics, and Computer Science Faculty Articles and Research

It is shown that the codewords of the binary and ternary Golay codes can be converted into rays in RP²³ and RP¹¹ that provide proofs of the Kochen-Specker theorem in real state spaces of dimensions 24 and 12, respectively. Some implications of these results are discussed.

What Is Nonclassical About Uncertainty Relations?, Lorenzo Catani, Matthew S. Leifer, Giovanni Scala, David Schmid, Robert W. Spekkens

Mathematics, Physics, and Computer Science Faculty Articles and Research

Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this perspective is undermined by the fact that there exist operational theories which exhibit nontrivial uncertainty relations but which are consistent with the classical worldview insofar as they admit of a generalized-noncontextual ontological model. This prompts the question of what aspects of uncertainty relations, if any, cannot be realized in …

The 'Quantal Newtonian' First Law: A Complementary Perspective To The Stationary-State Quantum Theory Of Electrons, Viraht Sahni

Publications and Research

A complementary perspective to the Göttingen-Copenhagen interpretation of stationary-state quantum theory of electrons in an electromagnetic field is described. The perspective, derived from Schrödinger-Pauli theory, is that of the individual electron via its equation of motion or ‘Quantal Newtonian’ First Law. The Law is in terms of ‘classical’ fields experienced by each electron: the sum of the external and internal fields vanishes. The external field is a sum of the electrostatic and Lorentz fields. The internal field is a sum of fields’ representative of Pauli and Coulomb correlations; kinetic effects; electron density; and internal magnetic component. The energy is obtained …

Methodologies For Quantum Circuit And Algorithm Design At Low And High Levels, Edison Tsai

Dissertations and Theses

Although the concept of quantum computing has existed for decades, the technology needed to successfully implement a quantum computing system has not yet reached the level of sophistication, reliability, and scalability necessary for commercial viability until very recently. Significant progress on this front was made in the past few years, with IBM planning to create a 1000-qubit chip by the end of 2023, and Google already claiming to have achieved quantum supremacy. Other major industry players such as Intel and Microsoft have also invested significant amounts of resources into quantum computing research.

Any viable computing system requires both hardware and …

Perspectives On Determinism In Quantum Mechanics: Born, Bohm, And The 'Quantal Newtonian' Laws, Viraht Sahni

Publications and Research

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen-Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a ‘probability amplitude’. A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper we present a new perspective on such determinism. The ideas are based on the equations of motion or ‘Quantal Newtonian’ Laws obeyed by each electron. These Laws, derived from the …

Quantum Field Theories, Topological Materials, And Topological Quantum Computing, Muhammad Ilyas

Dissertations and Theses

A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with the environment. It is a real challenge to completely isolate a quantum system to make it free of decoherence. This problem can be circumvented by the use of topological quantum phases of matter. These phases have quasiparticles excitations called anyons. The anyons are charge-flux composites and show exotic fractional statistics. When the order of exchange matters, then the anyons are called non-Abelian anyons. Majorana …

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

Relating The Finite-Volume Spectrum And The Two And Three-Particle S Matrix For Relativistic Systems Of Identical Scalar Particles, Raúl Briceño, Maxwell T. Hansen, Stephen R. Sharpe

Physics Faculty Publications

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicity L. This gives the relation between the finite-volume spectrum and the infinite-volume 2 → 2, 2 → 3, and 3 → 3 scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass m, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K matrix has no singularities below the three-particle threshold. The quantization condition is exact …

A Method For Achieving Analytic Formulas For Three Body Integrals Consisting Of Powers And Exponentials In All Three Interparticle Hyllerass Coordinates, Chris M. Keating

Dissertations and Theses

After an introduction to the variational principle of three body systems via the Helium atom, we present general analytical formulas for the radial parts of integrals that occur when three body systems are described using wave functions that consist of powers and exponentials in all three interparticle Hylleraas coordinates [Hylleraas1929]. This work is an extension of integrals given by Harris, Frolov and Smith, Jr. [Harris2004]. Specifically included are radial integrals encountered in calculations involving the dipole moment matrix element in Hylleraas coordinates that contain a function f(kr₁) (such as a spherical Bessel function) in addition to …

Four Tails Problems For Dynamical Collapse Theories, Kelvin J. Mcqueen

Philosophy Faculty Articles and Research

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails …

Identical Particles In Quantum Mechanics : Operational And Topological Considerations, Klil H. Neori

Legacy Theses & Dissertations (2009 - 2024)

This dissertation reports our investigation into the existence of anyons, which interpolate between bosons and fermions, in light of the Symmetrization Postulate, which states that only the two extremes exist. The Symmetrization Postulate can be understood as asserting that there are only two consistent ways of combining the behavior of distinguishable particles to obtain the behavior of identical ones. We showed that anyonic behavior then arises because of the way in which the probability amplitudes of distinguishable particles in two dimensions are affected by the topology of the space. These can then be combined in one of the ways arising …

Momentum And Spin In Entropic Quantum Dynamics, Shahid Nawaz

Legacy Theses & Dissertations (2009 - 2024)

We study quantum theory as an example of entropic inference. Our goal is to remove conceptual difficulties that arise in quantum mechanics. Since probability is a common feature of quantum theory and of any inference problem, we briefly introduce probability theory and the entropic methods to update probabilities when new information becomes available. Nelson's stochastic mechanics and Caticha's derivation of quantum theory are discussed in the subsequent chapters. Our first goal is to understand momentum and angular momentum within an entropic dynamics framework and to derive the corresponding uncertainty relations. In this framework momentum is an epistemic concept -- it …

A Gauge Theoretic Treatment Of Rovibrational Motion In Diatoms, Gregory Colarch

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Born-Oppenheimer approximation has long been the standard approach to solving the Schrödinger equation for diatomic molecules. In it, nuclear and electronic motions are separated into "slow" and "fast" degrees of freedom and couplings between the two are ignored. The neglect of non-adiabatic couplings leads to an incomplete description of diatomic motion, and in a more refined approach, non-adiabatic couplings are uncoupled by transforming the angular momentum of the molecule and electrons into the body-fixed frame.

In this thesis we examine a "modern" form of the Born-Oppenheimer approximation by exploiting a gauge theoretic approach in a description of molecular motion. …

Equivalent Dynamical Complexity In A Many-Body Quantum And Collective Human System, Neil F. Johnson, Josef Ashkenazi, Zhenyuan Zhao, Luis Quiroga

Physics Articles and Papers

Proponents of Complexity Science believe that the huge variety of emergent phenomena observed throughout nature, are generated by relatively few microscopic mechanisms. Skeptics however point to the lack of concrete examples in which a single mechanistic model manages to capture relevant macroscopic and microscopic properties for two or more distinct systems operating across radically different length and time scales. Here we show how a single complexity model built around cluster coalescence and fragmentation, can cross the fundamental divide between many-body quantum physics and social science. It simultaneously (i) explains a mysterious recent finding of Fratini et al. concerning quantum many-body …

Unitary-Quantum-Lattice Algorithm For Two-Dimensional Quantum Turbulence, Bo Zhang, George Vahala, Linda L. Vahala, Min Soe

Electrical & Computer Engineering Faculty Publications

Quantum vortex structures and energy cascades are examined for two-dimensional quantum turbulence (2D QT) at zero temperature. A special unitary evolution algorithm, the quantum lattice algorithm, is employed to simulate the Bose-Einstein condensate governed by the Gross-Pitaevskii (GP) equation. A parameter regime is uncovered in which, as in 3D QT, there is a short Poincare recurrence time. It is demonstrated that such short recurrence times are destroyed by stronger nonlinear interaction. The similar loss of Poincare recurrence is also seen in the 3D GP equation. Various initial conditions are considered in an attempt to discern if 2D QT exhibits inverse …

Poincare Recurrence And Spectral Cascades In Three-Dimensional Quantum Turbulence, George Vahala, Jeffrey Yepez, Linda L. Vahala, Min Soe, Bo Zhang, Sean Ziegeler

Electrical & Computer Engineering Faculty Publications

The time evolution of the ground state wave function of a zero-temperature Bose-Einstein condensate (BEC) gas is well described by the Hamiltonian Gross-Pitaevskii (GP) equation. Using a set of appropriately interleaved unitary collision-stream operators, a qubit lattice gas algorithm is devised, which on taking moments, recovers the Gross-Pitaevskii (GP) equation under diffusion ordering (time scales as length²). Unexpectedly, there is a class of initial states whose Poincaré recurrence time is extremely short and which, as the grid resolution is increased, scales with diffusion ordering (and not as length³). The spectral results of J. Yepez et al. …

Theoretical And Computational Study Of Time Dependent Scattering On A 2d Surface, Michael Sohn

UNLV Theses, Dissertations, Professional Papers, and Capstones

The quantum mechanical treatment of the elastic scattring of atoms from a crystal surface provides valuable information, such as surface properties and gas-surface interaction potentials. However, since it is based on the stationary state solution, it does not provide the details of the scattering process in the neighborhood of the surface, especially when atoms are physically adsorbed. In this thesis, the time evolution of the scattering process is treated in 2D with a model potential, V(x, z) = -|g|δ(z) + λδ(z)cos(2πx/a), using the Gaussian wave packet approach. The focus is on the case where the Gaussian wave packet makes a …

A General Quantum Mechanical Method To Predict Positron Spectroscopy, Paul E. Adamson

Theses and Dissertations

The nuclear-electronic orbital (NEO) method was modified and extended to positron systems. NEO - second-order Moeller-Plesset perturbation (MP2) energies and annihilation rates were calculated for the positronium hydride (PsH) system, and the effects of basis set size on correlation energies captured with the NEO-MP2 and NEO-full configuration interaction (FCI) methods are compared and discussed. Equilibrium geometries and vibrational energy levels were computed for the LiX and e⁺LiX (X = H, F, Cl) systems at the MP2 and NEO-MP2 levels. It was found that anharmonicity plays a significant role, specifically in the differences between the vibrational energy levels of …

Lattice Quantum Algorithm For The Schrodinger Wave Equation In 2+1 Dimensions With A Demonstration By Modeling Soliton Instabilities, Jeffrey Yepez, George Vahala, Linda L. Vahala

Electrical & Computer Engineering Faculty Publications

A lattice-based quantum algorithm is presented to model the non-linear Schrödinger-like equations in 2 + 1 dimensions. In this lattice-based model, using only 2 qubits per node, a sequence of unitary collide (qubit-qubit interaction) and stream (qubit translation) operators locally evolve a discrete field of probability amplitudes that in the long-wavelength limit accurately approximates a non-relativistic scalar wave function. The collision operator locally entangles pairs of qubits followed by a streaming operator that spreads the entanglement throughout the two dimensional lattice. The quantum algorithmic scheme employs a non-linear potential that is proportional to the moduli square of the wave function. …

Quantum Mechanical Calculations Of Monoxides Of Silicon Carbide Molecules, John W. Roberts Jr.

Theses and Dissertations

Modern semiconductor devices are principally made using the element silicon. In recent years, silicon carbide (SiC), with its wide band-gap, high thermal conductivity, and radiation resistance, has shown prospects as a semiconductor material for use in high temperature and radiation environments such as jet engines and satellites. A limiting factor in the performance of many SiC semiconductor components is the presence of lattice defects formed at oxide dielectric junctions during processing. Recent theoretical work has used small quantum mechanical systems embedded in larger molecular mechanics structures to attempt to better understand SiC surfaces and bulk materials and their oxidation. This …

Measurement Of Hyperfine Coupling Constants Of The 5d²D₃/₂ And 5d²D₅/₂ Levels In Atomic Cesium Using Polarization Quantum Beat Spectroscopy, Wo Yei

Physics Theses & Dissertations

Accurate measurements of hyperfine constants have revealed effects that can not be explained by a simple hydrogenic picture of the alkali atoms such as cesium [1-3]. More precise experimental results and theoretical treatments are in demand for the alkali elements, especially for atomic cesium because of its wide range of applications. Therefore, it is essential to understand its atomic and nuclear structure. Precision measurement of its excited-states properties such as hyperfine structure provides global information on nuclear charge and current distributions and also serves as a check to the theory and a calibration of calculated excited state wave functions. Accurate …

Compton's 'Crucial Test' - Theoretical Preconceptions And Experimental Interpretation, Roger H. Stuewer

Journal of the Minnesota Academy of Science

Arthur Holly Compton, as a result of his own research and confidence in the validity of classical electrodynamics, was convinced in 1921 that homogeneous x-rays and gamma rays could be affected in only two possible ways when passing through matter: either they gave rise to "truly scattered" radiation of the same wavelength as that of the incident rays, or they excited "fluorescent" radiation of a longer wavelength. When Compton was led to carry out experiments using homogeneous x-rays and actually found secondary radiation of longer wavelength, he regarded his result as a crucial test between the "truly scattered" and the …