Physical Sciences and Mathematics 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 …

Computational Methods For Propagation Of Optical Fields With The Angle-Impact Wigner Function, Jeremy Wittkopp

Legacy Theses & Dissertations (2009 - 2024)

In designing an optical setup for an experiment, one usually turns to simulations first in order to model the propagation of light through the proposed system. This way, the experimenter can determine if the system is operating as intended. In order for these simulations to be useful, they need to properly describe the propagation of light. In order to simplify calculations, most contemporary software makes assumptions on the nature of the light being propagated. Specifically, simulations typically consider optical fields that are beam-like (i.e., most of the rays comprising the field deviate only slightly in angle from the beam's primary …

Quantum Algorithms For Attacking Hardness Assumptions In Classical And Post‐Quantum Cryptography, J.-F. Biasse, X. Bonnetain, E. Kirshanova, A. Schrottenloher, Fang Song

Computer Science Faculty Publications and Presentations

In this survey, the authors review the main quantum algorithms for solving the computational problems that serve as hardness assumptions for cryptosystem. To this end, the authors consider both the currently most widely used classically secure cryptosystems, and the most promising candidates for post-quantum secure cryptosystems. The authors provide details on the cost of the quantum algorithms presented in this survey. The authors furthermore discuss ongoing research directions that can impact quantum cryptanalysis in the future.

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 Foundations Of Inference And Its Application To Fundamental Physics, Nicholas Matthew Carrara

Legacy Theses & Dissertations (2009 - 2024)

This thesis concerns the foundations of inference – probability theory,entropic inference, information geometry, etc. – and its application to the Entropic Dynamics (ED) approach to Quantum Mechanics (QM) [21, 22, 41, 53, 56–61, 150–153, 165, 195, 196, 268]. The first half of this thesis, chapters 2-6, concern the development of the inference framework. We begin in chapter 2 by discussing de- ductive inference, which involves formal logic and it’s role in access- ing the truth of propositions. We eventually discover that deductive inference is incomplete, in that it can’t address situations in which we have incomplete information. This necessitates a …

A New Look At The Quantum Liouville Theorem, P. T. Leung, G. I. Ni

Physics Faculty Publications and Presentations

We clarify certain confusions in the literature of the density operator in quantum mechanics, and demonstrate that the quantum Liouville theorem has the same form in both the Schrodinger and the Heisenberg pictures. Our starting point is to treat the density operator as an observable which has its specific time dependence in each of the two pictures. It is further shown that such a formulation will provide the exact correspondence between classical and quantum statistical mechanics with the Liouville theorem being interpreted as a conservation law, which is derivable from the equation of motion only in the quantum case.

On Basing One-Way Permutations On Np-Hard Problems Under Quantum Reductions, Nai-Hui Chia, Sean Hallgren, Fang Song

Computer Science Faculty Publications and Presentations

A fundamental pursuit in complexity theory concerns reducing worst-case problems to average-case problems. There exist complexity classes such as PSPACE that admit worst-case to average-case reductions. However, for many other classes such as NP, the evidence so far is typically negative, in the sense that the existence of such reductions would cause collapses of the polynomial hierarchy(PH). Basing cryptographic primitives, e.g., the average-case hardness of inverting one-way permutations, on NP-completeness is a particularly intriguing instance. As there is evidence showing that classical reductions from NP-hard problems to breaking these primitives result in PH collapses, it seems unlikely to base cryptographic …

Optical Stability Of 1,1′-Binaphthyl Derivatives, Nikolay V. Tkachenko, Steve Scheiner

Chemistry and Biochemistry Faculty Publications

The racemization process of various 1,1′-binaphthyl derivatives is studied by quantum calculations. The preferred racemization pathway passes through a transition state belonging to the C_i symmetry group. The energy barrier for this process is independent of solvation, the electron-withdrawing/releasing power of substituents, or their ability to engage in H-bonds within the molecule. The primary factor is instead the substituent size. The barrier is thus reduced when the −OH groups of 1,1′-bi-2-naphthol are replaced by H. There is a drop in the barrier also when the substituents are moved from the 2,2′ positions to 6,6′, where they will not come …

Infinite Mode Quantum Gaussian States., Tiju Cherian John Dr.

Doctoral Theses

No abstract provided.

Infinite-Randomness Fixed Point Of The Quantum Superconductor-Metal Transitions In Amorphous Thin Films, Nicholas A. Lewellyn, Ilana M. Percher, J. J. Nelson, Javier Garcia-Barriocanal, Irina Volotsenko, Aviad Frydman, Thomas Vojta, Allen M. Goldman

Physics Faculty Research & Creative Works

The magnetic-field-tuned quantum superconductor-insulator transitions of disordered amorphous indium oxide films are a paradigm in the study of quantum phase transitions and exhibit power-law scaling behavior. For superconducting indium oxide films with low disorder, such as the ones reported on here, the high-field state appears to be a quantum-corrected metal. Resistance data across the superconductor-metal transition in these films are shown here to obey an activated scaling form appropriate to a quantum phase transition controlled by an infinite-randomness fixed point in the universality class of the random transverse-field Ising model. Collapse of the field-dependent resistance vs temperature data is obtained …

Quantum Mechanical Studies Of N-H···N Hydrogen Bonding In Acetamide Derivatives And Amino Acids, Sandra J. Lundell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Proteins are made of vast chains of amino acids that twist and fold into intricate designs. These structures are held in place by networks of noncovalent interactions. One of these, the hydrogen bond, forms bridges between adjacent pieces of the protein chain and is one of the most important contributors to the shape and stability of proteins. Hydrogen bonds come in all shapes and sizes and a full understanding of these not only aids in our understanding of proteins in general but can bridge the gap to finding cures to many protein-related diseases, such as sickle-cell anemia. The primary aim …

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

Long-Range Interactions Of Hydrogen Atoms In Excited States. Iii. Ns−1s Interactions For N ≥ 3, Chandra M. Adhikari, V. Debierre, Ulrich D. Jentschura

Physics Faculty Research & Creative Works

The long-range interaction of excited neutral atoms has a number of interesting and surprising properties such as the prevalence of long-range oscillatory tails and the emergence of numerically large van der Waals C₆ coefficients. Furthermore, the energetically quasidegenerate nP states require special attention and lead to mathematical subtleties. Here we analyze the interaction of excited hydrogen atoms in nS states (3 ≤ n ≤ 12) with ground-state hydrogen atoms and find that the C6 coefficients roughly grow with the fourth power of the principal quantum number and can reach values in excess of 240000 (in atomic units) for states …

Long-Range Tails In Van Der Waals Interactions Of Excited-State And Ground-State Atoms, Ulrich D. Jentschura, V. Debierre

Physics Faculty Research & Creative Works

A quantum electrodynamic calculation of the interaction of an excited-state atom with a ground-state atom is performed. For an excited reference state and a lower-lying virtual state, the contribution to the interaction energy naturally splits into a pole term and a Wick-rotated term. The pole term is shown to dominate in the long-range limit, altering the functional form of the interaction from the retarded 1/R⁷ Casimir-Polder form to a long-range tail - provided by the Wick-rotated term - proportional to cos[2(E_m - E_n)R/(ħc)]/R², where E_m < E_n is the energy of a virtual state, …

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 …

Vibrational Energy Levels Of The Simplest Criegee Intermediate (Ch₂Oo) From Full-Dimensional Lanczos, Mctdh, And Multimode Calculations, Hua-Gen Yu, Steve Alexandre Ndengué, Jun Li, Richard Dawes, Hua Guo

Chemistry Faculty Research & Creative Works

Accurate vibrational energy levels of the simplest Criegee intermediate (CH₂OO) were determined on a recently developed ab initio based nine-dimensional potential energy surface using three quantum mechanical methods. the first is the iterative Lanczos method using a conventional basis expansion with an exact Hamiltonian. the second and more efficient method is the multi-configurational time-dependent Hartree (MCTDH) method in which the potential energy surface is refit to conform to the sums-of-products requirement of MCTDH. Finally, the energy levels were computed with a vibrational self-consistent field/virtual configuration interaction method in MULTIMODE. the low-lying levels obtained from the three methods are …

Kinetic Isotope Effect Of The ¹⁶O+³⁶O₂ And ¹⁸O+³²O₂ Isotope Exchange Reactions: Dominant Role Of Reactive Resonances Revealed By An Accurate Time-Dependent Quantum Wavepacket Study, Zhigang Sun, Dequan Yu, Wenbo Xie, Jiayi Hou, Richard Dawes, Hua Guo

Chemistry Faculty Research & Creative Works

The O + O₂ isotope exchange reactions play an important role in determining the oxygen isotopic composition of a number of trace gases in the atmosphere, and their temperature dependence and kinetic isotope effects (KIEs) provide important constraints on our understanding of the origin and mechanism of these and other unusual oxygen KIEs important in the atmosphere. This work reports a quantum dynamics study of the title reactions on the newly constructed Dawes-Lolur-Li-Jiang-Guo (DLLJG) potential energy surface (PES). The thermal reaction rate coefficients of both the 18O + 32O₂ and 16O + 36O₂ reactions obtained using the …

Signatures Of Chaos In The Dynamics Of Quantum Discord, Vaibhav Madhok, Vibhu Gupta, Denis-Alexandre Trottier, Shohini Ghose

Physics and Computer Science Faculty Publications

We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time-averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behavior of two-qubit discord versus entanglement of the two qubits as measured by the concurrence. Our results provide evidence of signatures of …

Class Of Unambiguous State Discrimination Problems Achievable By Separable Measurements But Impossible By Local Operations And Classical Communication, Scott M. Cohen

Physics Faculty Publications and Presentations

We consider an infinite class of unambiguous quantum state discrimination problems on multipartite systems, described by Hilbert space H, of any number of parties. Restricting consideration to measurements that act only on H, we find the optimal global measurement for each element of this class, achieving the maximum possible success probability of 1/2 in all cases. This measurement turns out to be both separable and unique, and by our recently discovered necessary condition for local quantum operations and classical communication (LOCC) it is easily shown to be impossible by any finite-round LOCC protocol. We also show that, quite generally, if …

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 …

A Quantum Theory Of Consciousness May Require A Paradigm Shift In Biology, Maurice Goodman

Articles

It is often assumed that the known physical laws form a closed system and are complete. It is also assumed that biological theories require no additional principles that are fundamental other than those we already know. Assumptions such as these are acting as a barrier to progress in biological theories and an understanding of consciousness. This paper examines the unexplained inconsistencies among fundamental particles and forces and the fundamental gaps in our knowledge of biology and the cell in particular that may impact on such progress. Also, the laws of quantum mechanics are examined and found to be grossly incomplete. …

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 …

Interpolation And Sampling On The Fock Space, Daniel F. Stevenson

Legacy Theses & Dissertations (2009 - 2024)

The theory interpolating and sampling sequences on spaces of analytic functions is one that has been widely studied and continues to produce open problems. In this dissertation we seek to further the study of these sequences in the Fock space setting.