Physics Commons^™

The Fourier–Legendre Series Of Bessel Functions Of The First Kind And The Summed Series Involving 1F2 Hypergeometric Functions That Arise From Them, Jack C. Straton

Physics Faculty Publications and Presentations

The Bessel function of the first kind JN^(kx) is expanded in a Fourier–Legendre series, as is the modified Bessel function of the first kind IN^(kx). The purpose of these expansions in Legendre polynomials was not an attempt to rival established numerical methods for calculating Bessel functions but to provide a form for JN^(kx) useful for analytical work in the area of strong laser fields, where analytical integration over scattering angles is essential. Despite their primary purpose, one can easily truncate the series at 21 terms to provide 33-digit accuracy that matches the IEEE extended precision in …

Integral Representations Over Finite Limits For Quantum Amplitudes, Jack C. Straton

Physics Faculty Publications and Presentations

We extend previous research to derive three additional M-1-dimensional integral representations over the interval [0,1]" The prior version covered the interval [0,∞]" role="presentation position: relative;">[0,∞][0,∞]. This extension applies to products of M Slater orbitals, since they (and wave functions derived from them) appear in quantum transition amplitudes. It enables the magnitudes of coordinate vector differences (square roots of polynomials) |x1−x2|=x12−2x1x2cosθ+_x22" to be shifted from disjoint products of functions into a single quadratic form, allowing for the completion of its square. The M-1-dimensional integral representations of M Slater orbitals that both this extension and the prior version introduce …

Economic Entanglement: The Quantum Race Between The United States And China, Isabella Willhite

Regis University Student Publications (comprehensive collection)

The United States and China are both currently home to the strongest economies and militaries in the world. Despite their interdependence, trade wars have escalated between the two countries in the past few years. While past trade wars have been focused on purely economic protectionism or ideological stances, the trade wars of today signify a shift towards protecting critical emerging technologies. The important emerging technology of today is quantum computing, which will forever change the way that computers encrypt, process, and decode information. The United States and China are on the eve of the “quantum race,” in which they will …

A Formalism For Extracting Track Functions From Jet Measurements, Kyle Lee, Ian Moult, Felix Ringer, Wouter J. Waalewijn

Physics Faculty Publications

The continued success of the jet substructure program will require widespread use of tracking information to enable increasingly precise measurements of a broader class of observables. The recent reformulation of jet substructure in terms of energy correlators has simplified the incorporation of universal non-perturbative matrix elements, so called “track functions”, in jet substructure calculations. These advances make it timely to understand how these universal non-perturbative functions can be extracted from hadron collider data, which is complicated by the use jet algorithms. In this paper we introduce a new class of jet functions, which we call (semi-inclusive) track jet functions, which …

Quantum Reality With Negative-Mass Particles, Mordecai Waegell, Eliahu Cohen, Avshalom C. Elitzur, Jeff Tollaksen, Yakir Aharonov

Mathematics, Physics, and Computer Science Faculty Articles and Research

Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric formulation to assign eigenvalues to unmeasured observables of a system, which results in logical paradoxes, and no clear physical picture. A top–down ontological model is introduced that treats the weak values of observables as physically real during the time between pre- and post-selection (PPS), which avoids these paradoxes. The generally delocalized rank-1 projectors of a quantum system describe its fundamental ontological elements, and the highest-rank projectors corresponding to …

A Quantum Approach To Language Modeling, Constantijn Van Der Poel

Dissertations, Theses, and Capstone Projects

This dissertation consists of six chapters. . . Chapter 1: We introduce language modeling, outline the software used for this thesis, and discuss related work. Chapter 2: We will unpack the transition from classical to quantum probabilities, as well as motivate their use in building a model to understand language-like datasets. Chapter 3: We motivate the Motzkin dataset, the models we will be investigating, as well as the necessary algorithms to do calculations with them. Chapter 4: We investigate our models’ sensitivity to various hyperparameters. Chapter 5: We compare the performance and robustness of the models. Chapter 6: We conclude …

Full Treatment Of The Thrust Distribution In Single Inclusive E⁺E⁻ → H X Processes, M. Boglione, Andrea Simonelli

Physics Faculty Publications

Extending the transverse momentum dependent factorization to thrust dependent observables entails a series of difficulties, ultimately associated to the behavior of soft radiation. As a consequence, the definition of the transverse momentum dependent functions has to be revised, while preserving (and possibly extending) their universality properties. Moreover, the regularization of the rapidity divergences generates non trivial correlations between rapidity and thrust. In this paper, we show how to deal with these correlations in a consistent treatment of the thrust dependence of e⁺e⁻ → h X cross section, where the hadron transverse momentum is measured with respect to …

Machine Learning-Based Jet And Event Classification At The Electron-Ion Collider With Applications To Hadron Structure And Spin Physics, Kyle Lee, James Mulligan, Mateusz Płoskoń, Felix Ringer, Feng Yuan

Physics Faculty Publications

We explore machine learning-based jet and event identification at the future Electron-Ion Collider (EIC). We study the effectiveness of machine learning-based classifiers at relatively low EIC energies, focusing on (i) identifying the flavor of the jet and (ii) identifying the underlying hard process of the event. We propose applications of our machine learning-based jet identification in the key research areas at the future EIC and current Relativistic Heavy Ion Collider program, including enhancing constraints on (transverse momentum dependent) parton distribution functions, improving experimental access to transverse spin asymmetries, studying photon structure, and quantifying the modification of hadrons and jets in …

Gluon Transverse-Momentum-Dependent Distributions From Large-Momentum Effective Theory, Ruilin Zhu, Yao Ji, Jian-Hui Zhang, Shuai Zhao

Physics Faculty Publications

We demonstrate that gluon transverse-momentum-dependent parton distribution functions (TMDPDFs) can be extracted from lattice calculations of appropriate Euclidean correlations in large-momentum effective theory (LaMET). Based on perturbative calculations of gluon unpolarized and helicity TMDPDFs, we present a matching formula connecting them and their LaMET counterparts, where the latter are renormalized in a scheme facilitating lattice calculations and converted to the MS ¯ scheme. The hard matching kernel is given up to one-loop level. We also show that the perturbative result is independent of the prescription used for the pinch-pole singularity in the relevant correlations. Our results offer a guidance for …

Rapidity-Only Tmd Factorization At One Loop, Ian Balitsky

Physics Faculty Publications

Typically, a production of a particle with a small transverse momentum in hadron-hadron collisions is described by CSS-based TMD factorization at moderate Bjorken x_B ~ 1 and by k_T-factorization at small x_B. A uniform description valid for all x_B is provided by rapidity-only TMD factorization developed in a series of recent papers at the tree level. In this paper the rapidity-only TMD factorization for particle production by gluon fusion is extended to the one-loop level.

An Integral Transform For Quantum Amplitudes, Jack C. Straton

Physics Faculty Publications and Presentations

The central impediment to reducing multidimensional integrals of transition amplitudes to analytic form, or at least to a fewer number of integral dimensions, is the presence of magnitudes of coordinate vector differences (square roots of polynomials) |x1−x2|2=x21−2x1x2cosθ+x2 √ in disjoint products of functions. Fourier transforms circumvent this by introducing a three-dimensional momentum integral for each of those products, followed in many cases by another set of integral transforms to move all of the resulting denominators into a single quadratic form in one denominator whose square my be completed. Gaussian transforms introduce a one-dimensional integral for each such product while squaring …

Approaching Quantum-Limited Electrometry In The Single-Photon Regime, Sisira Kanhirathingal

Dartmouth College Ph.D Dissertations

Mesoscopic quantum systems currently serve as essential building blocks in many quantum information and metrology devices. This thesis investigates the potential of quantum-limited detection in a mesoscopic electrometer named the cavity-embedded Cooper pair transistor (cCPT). As one application, this charge detector can act as the basis for an optomechanical system in the single-photon strong coupling regime. The realization of this scheme would entail near quantum-limited, ultra-sensitive electrometry at the single-photon level, the feasibility of which is studied at length in this thesis.

On the one hand, we approach this question using a fundamental, first-principles study, where an operator scattering model …

Perturbative Unitarity And Nec Violation In Genesis Cosmology, Yong Cai, Ji Xu, Shuai Zhao, Siyi Zhou

Physics Faculty Publications

Explorations of the violation of null energy condition (NEC) in cosmology could enrich our understanding of the very early universe and the related gravity theories. Although a fully stable NEC violation can be realized in the “beyond Horndeski” theory, it remains an open question whether a violation of the NEC is allowed by some fundamental properties of UV-complete theories or the consistency requirements of effective field theory (EFT). We investigate the tree-level perturbative unitarity for stable NEC violations in the contexts of both Galileon and “beyond Horndeski” genesis cosmology, in which the universe is asymptotically Minkowskian in the past. We …

The Entropic Dynamics Of Relativistic Quantum Fields In Curved Space-Time, Selman Ipek

Legacy Theses & Dissertations (2009 - 2024)

It has often been the case in history that the laws of physics have been used as the framework for understanding and implementing information processing. The tacit assumption is that the laws of physics are fundamental and that the notion of information is derived from these laws. Here we take the opposite view: the laws of physics are an application of the rules for processing information. The inferential framework of entropic dynamics (ED) has previously been developed by A. Caticha for the purposes of understanding and deriving quantum theory, in much the same way that E.T. Jaynes used the MaxEnt …

Towards Realism Interpretation Of Wave Mechanics Based On Maxwell Equations In Quaternion Space And Some Implications, Including Smarandache’S Hypothesis, Florentin Smarandache, Victor Christianto, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Measurement, Dissipation, And Quantum Control With Superconducting Circuits, Patrick Harrington

Arts & Sciences Electronic Theses and Dissertations

The interaction between a superconducting circuit and its environment can cause decoherence. However, interactions with an environment are necessary for quantum state preparation and measurement. Through the dynamics of open quantum systems, the environment is a resource to control and readout superconducting circuit states. I present an experimental result demonstrating qubit state stabilization from engineered dissipation with a microwave photonic crystal. In addition, I discuss the statistical arrow of time in the dynamics of continuous quantum measurement. These results demonstrate an interplay between open quantum system dynamics and statistics, which highlights the role of both dissipation and measurement for quantum …

Production Of Entangled Photons Via Spontaneous Parametric Down-Conversion, Logan P. Kaelbling

Senior Projects Spring 2020

Quantum entanglement, a phenomenon in which the behavior of one particle is somehow immediately correlated with and informed by what is happening to a partner particle a long distance away, has been a pivotal part of the formulation of quantum theory as we know it today and is currently generating many promising avenues of research. As such, finding ways to reliably and inexpensively generate systems of entangled particles for research purposes has become crucial. For my project, I attempt to set up a system that generates energy- and polarization-entangled photons via a technique called spontaneous parametric down conversion. This method …

Polarization Of Majorana Fermions In A Background Current, Lukas Karoly, David C. Latimer

Summer Research

A Majorana fermion is a particle which is its own antiparticle. As a consequence, their electromagnetic interactions are minimal. Because of this, they are a good candidate for dark matter with their sole static electromagnetic property being their anapole moment. The annihilation rate of Majorana fermions depends on whether their anapole moments are aligned (polarized) or anti-aligned (unpolarized). It is therefore important to understand how Majorana fermions polarize to better understand their annihilation rates. This can help us further understand and detect dark matter. Using Feynman diagrams, we calculate the cross section for the interaction between a Majorana fermion and …

Quantum Correlations Between The Light And Kilogram-Mass Mirrors Of Ligo, Haocun Yu, L. Mcmuller, M. Tse, L. Barsotti, N. Mavalvala, J. Betzwieser, C. D. Blair, S. E. Dwyer, A. Effler, K. E. Ramirez

Physics and Astronomy Faculty Publications and Presentations

Measurement of minuscule forces and displacements with ever greater precision encounters a limit imposed by a pillar of quantum mechanics: the Heisenberg uncertainty principle. A limit to the precision with which the position of an object can be measured continuously is known as the standard quantum limit (SQL) [1–4]. When light is used as the probe, the SQL arises from the balance between the uncertainties of photon radiation pressure imposed on the object and of the photon number in the photoelectric detection. The only possibility surpassing the SQL is via correlations within the position/momentum uncertainty of the object and the …

Anomalous Stranski-Krastanov Growth Of (111)-Oriented Quantum Dots With Tunable Wetting Layer Thickness, Christopher F. Schuck, Simon K. Roy, Trent Garrett, Paul J. Simmonds

Materials Science and Engineering Faculty Publications and Presentations

Driven by tensile strain, GaAs quantum dots (QDs) self-assemble on In_0.52Al_0.48As(111)A surfaces lattice-matched to InP substrates. In this study, we show that the tensile-strained self-assembly process for these GaAs(111)A QDs unexpectedly deviates from the well-known Stranski-Krastanov (SK) growth mode. Traditionally, QDs formed via the SK growth mode form on top of a flat wetting layer (WL) whose thickness is fixed. The inability to tune WL thickness has inhibited researchers’ attempts to fully control QD-WL interactions in these hybrid 0D-2D quantum systems. In contrast, using microscopy, spectroscopy, and computational modeling, we demonstrate that for GaAs(111)A QDs, we …

New Tests Of General Relativity, Quentin Bailey

Quentin Bailey

The last decade has seen a rapid increase in the number of precision tests of relativity. This research has been motivated by the intriguing possibility that tiny deviations from relativity might arise in the underlying theory that is widely believed to successfully mesh General Relativity (GR) with quantum physics. Many of these tests have been analyzed within an effective field theory framework which generically describes possible deviations from exact relativity and contains some traditional test frameworks as limiting cases. One part of the activity has been a resurgence of interest in tests of relativity in the Minkowski-spacetime context, where Lorentz …

Full Dyon Excitation Spectrum In Extended Levin-Wen Models, Yuting Hu, Alexandra Tebbs, Yong-Shi Wu

Mathematics and Statistics Faculty Publications

In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two-dimensional topological phases, it is relatively easy to describe only single-fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological phases, an extension of the LW models is proposed in this paper. We first enlarge the Hilbert space with adding a tail on one of the edges of each trivalent vertex to describe the internal charge degrees of freedom at the vertex. Then, we study the full dyon spectrum of the extended LW models, including …

Is Qbism The Future Of Quantum Physics?, Kelvin J. Mcqueen

Philosophy Faculty Articles and Research

A review of Hans Christian von Baeyer’s QBism: The Future of Quantum Physics.

Mermin Inequalities For Perfect Correlations In Many-Qutrit Systems, Jay Lawrence

Dartmouth Scholarship

The existence of Greenberger-Horne-Zeilinger (GHZ) contradictions in many-qutrit systems was a long-standing theoretical question until its (affirmative) resolution in 2013. To enable experimental tests, we derive Mermin inequalities from concurrent observable sets identified in those proofs. These employ a weighted sum of observables, called M, in which every term has the chosen GHZ state as an eigenstate with eigenvalue unity. The quantum prediction for M is then just the number of concurrent observables, and this grows asymptotically as 2N/3 as the number of qutrits N→∞. The maximum classical value falls short for every N≥3, so that the quantum to classical …

Operator Locality In The Quantum Simulation Of Fermionic Models, Vojtěch Havlíček, Matthias Troyer, James D. Whitfield

Dartmouth Scholarship

Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of qubits. This overhead can be a hindrance to implementation of qubit-based quantum simulators, especially in the analog context. Here we thus review and analyze alternative fermion-to-qubit mappings, including the two approaches by Bravyi and Kitaev and the Auxiliary Fermion transformation. The Bravyi-Kitaev transform is reformulated in terms of a classical data structure and generalized to achieve a further locality improvement for local fermionic models on a …

Review Of Qbism: The Future Of Quantum Physics, Matthew S. Leifer

Mathematics, Physics, and Computer Science Faculty Articles and Research

A review of QBism: The Future of Quantum Physics by Hans Christian von Baeyer.

Local Spin Operators For Fermion Simulations, James D. Whitfield, Vojtěch Havlíček, Matthias Troyer

Dartmouth Scholarship

Digital quantum simulation of fermionic systems is important in the context of chemistry and physics. Simulating fermionic models on general purpose quantum computers requires imposing a fermionic algebra on qubits. The previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two techniques for accomplishing this task. Here, we reexamine an auxiliary fermion construction which maps fermionic operators to local operators on qubits. The local simulation is performed by relaxing the requirement that the number of qubits should match the number of single-particle states. Instead, auxiliary sites are introduced to enable nonconsecutive fermionic couplings to be simulated with constant low-rank tensor products on …

Exact Solution Of Quadratic Fermionic Hamiltonians For Arbitrary Boundary Conditions, Abhijeet Alase, Emilio Cobanera, Gerardo Ortiz, Lorenza Viola

Dartmouth Scholarship

We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D−1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect …

Dynamical Decoupling Sequences For Multi-Qubit Dephasing Suppression And Long-Time Quantum Memory, Gerardo A. Paz-Silva, Seung-Woo Lee, Todd J. Green, Lorenza Viola

Dartmouth Scholarship

We consider a class of multi-qubit dephasing models that combine classical noise sources and linear coupling to a bosonic environment, and are controlled by arbitrary sequences of dynamical decoupling pulses. Building on a general transfer filter-function framework for open-loop control, we provide an exact representation of the controlled dynamics for arbitrary stationary non-Gaussian classical and quantum noise statistics, with analytical expressions emerging when all dephasing sources are Gaussian. This exact characterization is used to establish two main results. First, we construct multi-qubit sequences that ensure maximum high-order error suppression in both the time and frequency domain and that can be …

Fundamental Awareness: A Framework For Integrating Science, Philosophy And Metaphysics, Neil D. Theise, Menas Kafatos

Mathematics, Physics, and Computer Science Faculty Articles and Research

The ontologic framework of Fundamental Awareness proposed here assumes that non-dual Awareness is foundational to the universe, not arising from the interactions or structures of higher level phenomena. The framework allows comparison and integration of views from the three investigative domains concerned with understanding the nature of consciousness: science, philosophy, and metaphysics. In this framework, Awareness is the underlying reality, not reducible to anything else. Awareness and existence are the same. As such, the universe is non-material, self-organizing throughout, a holarchy of complementary, process driven, recursive interactions. The universe is both its own first observer and subject. Considering the world …