Quantum Physics Commons^™

Differentiating The Impossible: Feynman's Trick In Applications Of Modern Physics, Yaohua Zhao

Discovery Day - Daytona Beach

We discuss Feynman’s method of differentiating with respect to a parameter inside an integral and explore its significance on selective topics of modern physics. This powerful technique allows us to integrate functions that may seem impossible. Depending on the underlying parameters, the Feynman method becomes a unifying framework that connects mathematical concepts to many parameter-dependent equations in modern physics. In statistical mechanics, this appears directly in the partition function, where derivatives with respect to temperature-related parameters yield thermodynamic quantities such as internal energy and heat capacity; this demonstrates how parameter dependence gives rise to macroscopic behaviors observable at a larger …

Momentum Space Algorithm For Electronic Structure Of Double-Incommensurate Trilayer Graphene, Kenneth Silver Beard

LSU Doctoral Dissertations

Numerical algorithms for computing the electronic structure of incommensurate 2D-materials using ab initio models are critical for predicting material properties and guiding experiments. For bilayers, momentum space and continuum models have been introduced to approximate observables of ab initio tight-binding models using a momentum description, despite the lack of periodicity in the tight-binding model required for Bloch theory. A similar structure has been introduced for double-incommensurate trilayers using a continuum model, where the three lattices are mutually incommensurate. However, this description leads to a four-dimensional lattice space, and numerical convergence of the density of states has been observed to be …

Non-Redundant Rovibrational Hamiltonians By Molien Generating Functions And Gröbner-Basis Reduction, Leandro Ajo

University Libraries Undergraduate Research Award

High-resolution molecular spectroscopy requires an effective Hamiltonian whose operator content is both complete, containing every term allowed by molecular symmetry and nonredundant, free of any algebraically dependent operators that would cause ill-conditioned parameter fits. Traditional derivations based on Van Vleck contact transformations satisfy neither criterion automatically. This paper develops a rigorous, algorithmic pipeline that guarantees both properties simultaneously. Starting from the permutation– inversion (PI) group GPI of a molecule (Longuet-Higgins, 1963), we apply Molien’s theorem (Molien, 1897) to the symplectic normal-coordinate representation to obtain the vibrational generating function Φvib(t); integrate over the Haar measure of SO(3) (Weyl, 1946) to obtain …

Extending The Geometric Phase To Relativistic Spacetime, Sajid Raihan Akash

Department of Physics and Astronomy: Dissertations, Theses, and Student Research

The Berry phase [3] is traditionally understood as a geometric phase acquired during cyclic adiabatic evolution, often interpreted as the flux of an effective “magnetic field” through a solid angle in parameter space. In this thesis, we investigate situations in which a geometric phase arises even when no spatial solid angle is enclosed, revealing the limitations of the standard purely spatial interpretation. We first review the Berry phase for a spin-½ particle in a slowly varying magnetic field and analyze scenarios in which the system’s eigenstate is changed during the adiabatic evolution. We show that the resulting phase can be …

On Quantum Processes And The Epistemic Constraints, Varun Immanuel Premkumar Immanuel

Electronic Theses & Dissertations (2024 - present)

This doctoral dissertation on the foundations of quantum theory tells the story of a conceptual protagonist I have called “Epistemic Constraint.” Here, epistemic constraints are the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described.

The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form …

Quantum Mechanics As A Framework For Data Assimilation And Its Application To Atmospheric Parameterization, David Freeman

Dartmouth College Ph.D Dissertations

Quantum mechanics, as a mathematical system, can be understood as a generalization of classical probability theory. Quantum Mechanical Data Assimilation (QMDA) is a method in which classical dynamical systems are embedded into a quantum mechanical setting, with an associated data assimilation scheme leveraging the operator algebraic setting. In this dissertation, the algebraic structure underlying the operator theoretic formulation of QMDA is discussed. A procedure for closure of dynamical systems based on QMDA, known as Quantum Mechanical Closure (QMCl), is then constructed, and the procedures for constructing the quantum embeddings and implementing QMCl in practice are laid out and implemented for …

A Mathematical Frameworks For Singular, Nonlinear Phenomena: Applications To Nematocyst Firing And Inhomogeneous Nls With Coulomb Potential, Abdulrahman Alharbi

Theses and Dissertations

Nematocysts are specialized cellular organelles found in all cnidarians, including corals and jellyfish, as well as in some single-celled protists such as dinoflagellates. These organelles display remarkable diversity in morphology and function, playing roles in prey capture and defense. The firing of a nematocyst is one of the fastest accelerations in nature, yet the underlying physical mechanisms remain not fully understood. In this work, we address key questions: how sufficient force is generated to overcome the fluid boundary layer, whether fluid–structure interaction models can reproduce observed dynamics, and what mechanisms trigger discharge.

Our research investigates models based on osmotic pressure …

Entropic Dynamics Approach To The Classical Limit Of Quantum Mechanics: Decoupling Of The Center Of Mass Motion For A Mesoscopic Particle, Fatimah Judayba

Electronic Theses & Dissertations (2024 - present)

In the Entropic Dynamics (ED) approach, quantum mechanics is derived from the principles of entropic inference and information geometry. The ED approach differs from other interpretations by making a clear commitment to distinguishing which variables are ontic (real) and which are epistemic. The classical limit for the center of mass (CM) coordinate is achieved for a large number of particles, M →∞, while Planck’s constant ℏ remains finite. Typically, the emergence of the classical limit requires decoherence through interactions with the external environment. In this work, we investigate whether the classical behavior of the CM coordinate in a mesoscopic system …

Degeneracies In A Weighted Sum Of Two Squares, Ishan V. Ramesh

Rose-Hulman Undergraduate Mathematics Journal

This work is an attempt to classify and quantify instances when a weighted sum of two squares of positive integers, 3n2 1 +n2 2, can be realized in more than one way. Our project was inspired by a particular study of two-dimensional quantum billiards [S. G. Jackson, H. Perrin, G. E. Astrakharchik, and M. Olshanii, SciPost Phys. Core 7, 062 (2024)] where the weighted sums of interest represents an energy level with the two integers being the billiard’s quantum numbers; there, the 3-fold degeneracies seem to dominate the energy spectrum. Interestingly, contrary to the conventional paradigm, these degeneracies are not …

An Alternative Approach To Non-Relativistic Quantum Mechanics In Curved Space, Robert A. Hulsey

Dissertations

In the research presented in this dissertation, we propose an alternative formulation of non-relativistic quantum mechanics in curved spaces (Riemannian manifolds). Some toy quantum models (2D quantum harmonic oscillator in Poincaré half-plane model and the flat chart model of hyperbolic 2-space) are studied to understand the physical implications of this alternative formulation.

Basic Theory And Implementations Of Quantum Error Correction, Derek Rodriguez

Undergraduate Theses, Capstones, and Recitals

The introduction of quantum computing has presented algorithmic solutions to computationally difficult challenges that are far more efficient than those of classical computers. These algorithms leverage the properties of quantum mechanics to manipulate the quantum properties of subatomic particles, requiring immense precision and stability. Current quantum hardware, however, is too noisy and introduces too many errors for these algorithms to be useful in practice, necessitating the use of error correction algorithms. This field survey seeks to introduce various principles of quantum mechanics relevant to quantum computing and quantum error correction (QEC), detail the implementation and motivations of a basic QEC …

Analyticity And Supershift With Regular Sampling, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Alain Yger

Mathematics, Physics, and Computer Science Faculty Articles and Research

The notion of supershift (in itself a generalization of the notion of superoscillation arising in quantum mechanics) expresses the fact that the sampling of a function in an interval allows to compute the values of the function far from the interval. In this paper, we study the relation between supershift and real analyticity. We use a classical result due to Serge Bernstein to show that real analyticity for a complex-valued function implies a strong form of supershift. On the other hand, we use a parametric version of a result by Leonid Kantorovitch to show that the converse is not true. …

Fiber Bundles Of The Complex Projective Space And Their Relation To Quantum Physics, Emily Wessman

Student Research Symposium

The complex projective space CPⁿ is the space of lines through the origin in Cⁿ⁺¹ with an equivalence relation defined by Z ~ λZ' for λ ∈ C*. We define the points under the equivalence relation as homogeneous coordinates, represented by [Z₀ : Z₁ : ... Z_n]. Since all Z,sub>i cannot equal zero, we can find a unique set of n coordinates (z₁,...,z_n) such that [Z₀ : Z₁ : ... : Z_n] ~ [1 : z₁ : ... : z_n] where z …

32 - Nested Two Level Decomposition For Quantum Computing, Andrew Maciejunes, John Stenger, Dan Gunlycke, Nikos Chrisochoides

Undergraduate Research Symposium

Abstract—We present a two-level decomposition strategy for solving the Vehicle Routing Problem (VRP) using the Quantum Approximate Optimization Algorithm (QAOA). A Problem-Level Decomposition (PLD) partitions a 9-node (72-qubit) VRP into smaller Traveling Salesman Problem (TSP) instances. Each TSP is then further simplified via Circuit-Level Decomposition (CLD), enabling execution on near-term quantum devices. Our approach achieves up to 90% reductions in circuit depth and qubit count. These results demonstrate the feasibility of solving VRPs previously too complex for quantum simulators and provide early evidence of potential quantum utility.

Mathematics And Determinism: Chaos, Quantum Mechanics, And The Limits Of Predictive Structure, Jackson T. Salumbides

CMC Senior Theses

This thesis examines the relationship between mathematics and determinism by analyzing how chaos theory, quantum mechanics, and formal mathematical limits challenge traditional conceptions of predictability and causal structure. Chaos theory shows that deterministic systems can exhibit practical unpredictability due to sensitivity to initial conditions. Quantum mechanics introduces probabilistic outcomes that complicate deterministic interpretation, though alternative frameworks such as Bohmian mechanics and superdeterminism attempt to restore determinism at conceptual cost. Additionally, results from mathematical logic, including Gödel’s incompleteness theorems and Turing’s undecidability, demonstrate intrinsic limitations on what can be deduced or computed, even in fully deterministic systems. By synthesizing these areas, …

0th Order Solutions Of The Wavefunctions For The Quantum Elliptical Box And Microstrip Antenna, Nishtha Tikalal

Honors Undergraduate Theses

For a quantum particle confined to a two-dimensional elliptical box or electromagnetic wave in a microstrip antenna, geometrical and boundary condition interplay result in a spectrum of spatial patterns. Due to the asymmetrical nature of the ellipse, we are faced with continuous symmetry reductions, leaving both degenerate and nondegenerate solutions. Here, we present a complete derivation of an analytical solution and visualizations of the fundamental wavefunctions for both Dirichlet and Neumann boundary conditions respectively corresponding to the quantum elliptical box and the elliptical microstrip antenna.

We demonstrate that the eigenmodes, governed by eccentricity, directly correspond to the modal field distributions …

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 …

A Thesis, Or Digressions On Sculptural Practice: In Which, Concepts & Influences Thereof Are Explained, Set Forth, Catalogued, Or Divulged By Way Of Commentaries To A Poem, First Conceived By The Artist, Fed Through Chatg.P.T., And Re-Edited By The Artist, To Which Are Added, Annotated References, Impressions And Ruminations Thereof, Also Including Private Thoughts & Personal Accounts Of The Artist, Jaimie An

Masters Theses

This thesis is an exercise in, perhaps a futile, attempt to trace just some of the ideas, stories, and musings I might meander through in my process. It’s not quite a map, nor is it a neat catalogue; it is a haphazard collection of tickets and receipts from a travel abroad, carelessly tossed in a carry-on, only to be stashed upon returning home. These ideas are derived from much greater thinkers and authors than myself; I am a mere collector or a translator, if that, and not a very good one, for much is lost. I do not claim comprehensive …

Nidus Idearum. Scilogs, Xiii: Structure / Neutrostructure / Antistructure, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this thirteenth book of scilogs – one may find topics on Neutrosophy, Plithogeny, Physics, Mathematics, Philosophy – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on. It presents new types of soft sets and new types of topologies.

Exchanging ideas with Mohammad Abobala, Ishfaq Ahmad, Ibrahim M. Almanjahie, Fatimah Alshahrani, Nizar Altounji, Muhammad Aslam, Said Broumi, Victor Christianto, R. Diksh, Feng Liu, Frank Julian Gelli, Erick Gonzalez Caballero, Riad Hamido, Yaser Al-Hasan, Ahmed Hatip, Yasin Karmouta, Nivetha Martin, Preda Mihăilescu, V. Lakshmana Gomathi Nayagam, Ze Carlos Tiago de …

Solutions To The Kaluza-Klein Field Equations, Abel Eshete

All Graduate Theses, Dissertations, and Other Capstone Projects

This Alternate Paper Plan explores Kaluza-Klein theory, a multidimensional framework designed to unify Einstein’s gravitational field theory and Maxwell’s electromagnetic field theory. The objectives of this research can be summarized in two key areas: The first objective is to present a comprehensive introduction to the compactified Kaluza-Klein theory. The second aim involves the application of differential geometry, specifically E ́lie Cartan’s tetrad formalism, to derive exact solutions in two distinct scenarios: a. A Levi-Civita spacetime, b. A general spherical system. Furthermore, Lagrangian and Hamiltonian formalism are utilized to define stability conditions and describe gravitational lensing and Precession of Perihelion within …

Plausible Photomolecular Effect And Microwave In Phase Transition Of Water As A New Dawn For Renewable Energy And Ensemble-Holistic Approach To Health Management, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Interaction among light and water molecules have baffled scientists for many decades, and even centuries. In this regards, photons in the visible spectrum, where bulk water normally doesn't absorb light, can surprisingly cleave off large water clusters from the water-vapor interface, according to a recent study by Tu and Chen (2023). This discovery, termed the "photomolecular effect," opens exciting possibilities for not only revolutionizing renewable energy but also paving the way for a more integrated-ensemble approach to health management (cf. Smarandache & Christianto, 2010; Tu & Chen, 2023; Tu et al., 2024). In a sense, other than with green or …

Progress In Physics: Twentieth Year Of Publication, Florentin Smarandache, Andreas Ries, Pierre Millette, Ebenezer Chifu

Branch Mathematics and Statistics Faculty and Staff Publications

The journal Progress in Physics was created in January 2005 on behalf of many influential scientists with whom we were in correspondence. The main reason was that publications in other journals were allowed only if the submitter was affiliated with a scientific institution or research organization. Given this situation, many working scientists finding themselves partially employed or unemployed, such as in between research grants, find themselves unable to publish their research results. Even e-print archives such as Cornell’s arXiv required scientific affiliation and still follow this policy.

Unveiling Quantum Communication: From Bell's Inequality To Neutrosophic Logic, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this mini-review, we delve into the intriguing realm of quantum communication, spurred by China's recent development of the Tiantong communication satellite. This satellite, shrouded in secrecy, hints at a revolutionary approach to communication that transcends the limitations of conventional signal transmission. We explore the foundational concepts of Bell's inequality and neutrosophic logic, elucidating their roles in understanding the non-local phenomena of quantum entanglement and its potential for secure and rapid communication. Additionally, we examine the connection between Bell's inequality and Shannon information entropy, unveiling the intricate relationship between quantum mechanics and information theory. Through this exploration, we glimpse a …

Continuous-Variable Quantum Computation Of The O(3) Model In 1+1 Dimensions, Raghav G. Jha, Felix Ringer, George Siopsis, Shane Thompson

Physics Faculty Publications

We formulate the O(3) nonlinear sigma model in 1+1 dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous-variable (CV) approach to quantum computing. We construct the ground state and excited states using the coupled-cluster Ansatz and find excellent agreement with the exact diagonalization results for a small number of lattice sites. We then present the simulation protocol for the time evolution of the model using CV gates and obtain numerical results using a photonic quantum simulator. We …

Effective Non-Hermiticity And Topology In Markovian Quadratic Bosonic Dynamics, Vincent Paul Flynn

Dartmouth College Ph.D Dissertations

Recently, there has been an explosion of interest in re-imagining many-body quantum phenomena beyond equilibrium. One such effort has extended the symmetry-protected topological (SPT) phase classification of non-interacting fermions to driven and dissipative settings, uncovering novel topological phenomena that are not known to exist in equilibrium which may have wide-ranging applications in quantum science. Similar physics in non-interacting bosonic systems has remained elusive. Even at equilibrium, an "effective non-Hermiticity" intrinsic to bosonic Hamiltonians poses theoretical challenges. While this non-Hermiticity has been acknowledged, its implications have not been explored in-depth. Beyond this dynamical peculiarity, major roadblocks have arisen in the search …

Applying Hallgren’S Algorithm For Solving Pell’S Equation To Finding The Irrational Slope Of The Launch Of A Billiard Ball, Sangheon Choi

Mathematical Sciences Technical Reports (MSTR)

This thesis is an exploration of Quantum Computing applied to Pell’s equation in an attempt to find solutions to the Billiard Ball Problem. Pell’s equation is a Diophantine equation in the form of x² − ny² = 1, where n is a given positive nonsquare integer, and integer solutions are sought for x and y. We will be applying Hallgren’s algorithm for finding irrational periods in functions, in the context of billiard balls and their movement on a friction-less unit square billiard table. Our central research question has been the following: Given the cutting sequence of the billiard …

Algebraic Tunnelling, Gaurab Sedhain

2023 REYES Proceedings

We study the quantum phenomenon of tunnelling in the framework of algebraic quantum theory, motivated by the tunnelling aspects of false vacuum decay. We see that resolvent C*-algebra, proposed relatively recently by Buchholz and Grundling rather than Weyl algebra provides an appropriate framework for treating the dynamics of non-free quantum mechanical system as an algebraic automorphism. At the end, we propose to investigate false vacuum decay in algebraic quantum field theoretic setting in terms of the two-point correlation function which gives us the tunneling probability, with the corresponding C*-algebraic construction.

The Fluid Margin Between Physical Causal Closure And Non-Physical Causal Closure, Extended To The Neutrosophic Causal Closure Principle, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We plead for a fluid margin, or mixed/indeterminate buffer zone, between Physical and Non-Physical Causal Closures, and for a Neutrosophic Causal Closure Principle claiming that the chances of all physical effects are determined by their prior partially physical and partially non-physical causes.

The Mceliece Cryptosystem As A Solution To The Post-Quantum Cryptographic Problem, Isaac Hanna

Senior Honors Theses

The ability to communicate securely across the internet is owing to the security of the RSA cryptosystem, among others. This cryptosystem relies on the difficulty of integer factorization to provide secure communication. Peter Shor’s quantum integer factorization algorithm threatens to upend this. A special case of the hidden subgroup problem, the algorithm provides an exponential speedup in the integer factorization problem, destroying RSA’s security. Robert McEliece’s cryptosystem has been proposed as an alternative. Based upon binary Goppa codes instead of integer factorization, his cryptosystem uses code scrambling and error introduction to hinder decrypting a message without the private key. This …

Classification Of Pixel Tracks To Improve Track Reconstruction From Proton-Proton Collisions, Kebur Fantahun, Jobin Joseph, Halle Purdom, Nibhrat Lohia

SMU Data Science Review

In this paper, machine learning techniques are used to reconstruct particle collision pathways. CERN (Conseil européen pour la recherche nucléaire) uses a massive underground particle collider, called the Large Hadron Collider or LHC, to produce particle collisions at extremely high speeds. There are several layers of detectors in the collider that track the pathways of particles as they collide. The data produced from collisions contains an extraneous amount of background noise, i.e., decays from known particle collisions produce fake signal. Particularly, in the first layer of the detector, the pixel tracker, there is an overwhelming amount of background noise that …