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Full-Text Articles in Physics

H-Atom Ladder Operator Revisited, Carl W. David Aug 2020

H-Atom Ladder Operator Revisited, Carl W. David

Chemistry Education Materials

An error laden note (Am. J. Phys., 34, 984,(1966)) concerning the ladder operator solution to the hydrogen atom electronic energy levels is corrected.


Contact In The Unitary Fermi Gas Across The Superfluid Phase Transition, S. Jensen, Christopher N. Gilbreth, Y. Alhassid Jul 2020

Contact In The Unitary Fermi Gas Across The Superfluid Phase Transition, S. Jensen, Christopher N. Gilbreth, Y. Alhassid

All Faculty Scholarship for the College of the Sciences

A quantity known as the contact is a fundamental thermodynamic property of quantum many-body systems with short-range interactions. Determination of the temperature dependence of the contact for the unitary Fermi gas of infinite scattering length has been a major challenge, with different calculations yielding qualitatively different results. Here we use finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods on the lattice within the canonical ensemble to calculate the temperature dependence of the contact for the homogeneous spin-balanced unitary Fermi gas. We extrapolate to the continuum limit for 40, 66, and 114 particles, eliminating systematic errors due to finite-range effects. We observe ...


Noncontextuality Inequalities From Antidistinguishability, Matthew S. Leifer, Cristhiano Duarte Jun 2020

Noncontextuality Inequalities From Antidistinguishability, Matthew S. Leifer, Cristhiano Duarte

Mathematics, Physics, and Computer Science Faculty Articles and Research

Noncontextuality inequalities are usually derived from the distinguishability properties of quantum states, i.e., their orthogonality. Here, we show that antidistinguishability can also be used to derive noncontextuality inequalities. The Yu-Oh 13-ray noncontextuality inequality can be rederived and generalized as an instance of our antidistinguishability method. For some sets of states, the antidistinguishability method gives tighter bounds on noncontextual models than just considering orthogonality, and the Hadamard states provide an example of this. We also derive noncontextuality inequalities based on mutually unbiased bases and symmetric informationally complete positive operator-valued measures. Antidistinguishability based inequalities were initially discovered as overlap bounds for ...


Non-Adiabatic Quantum Dynamics Of The Ultracold Li+Lina→ Li2+Na Chemical Reaction, B. K. Kendrick, M. Li, H. Li, S. Kotochigova, J. F.E. Croft, Balakrishnan Naduvalath Jun 2020

Non-Adiabatic Quantum Dynamics Of The Ultracold Li+Lina→ Li2+Na Chemical Reaction, B. K. Kendrick, M. Li, H. Li, S. Kotochigova, J. F.E. Croft, Balakrishnan Naduvalath

Chemistry and Biochemistry Faculty Publications

We report non-adiabatic dynamics of the Li+LiNa→Li2+Na chemical reaction at cold and ultracold temperatures employing accurate ab initio electronic potential energy surfaces in a quantum dynamics formulation employing a diabatic representation. Results are compared against those from a single adiabatic ground state potential energy surface and a universal model based on the long-range interaction potential. We discuss signatures of non-universal behavior in the total rate coefficients as well as strong non-adiabatic effects in the state-to-state rotationally resolved rate coefficients.


Quantum Computing And Quantum Algorithms, Daniel Serban Apr 2020

Quantum Computing And Quantum Algorithms, Daniel Serban

Senior Honors Theses

The field of quantum computing and quantum algorithms is studied from the ground up. Qubits and their quantum-mechanical properties are discussed, followed by how they are transformed by quantum gates. From there, quantum algorithms are explored as well as the use of high-level quantum programming languages to implement them. One quantum algorithm is selected to be implemented in the Qiskit quantum programming language. The validity and success of the resulting computation is proven with matrix multiplication of the qubits and quantum gates involved.


Magnetic Forces In The Absence Of A Classical Magnetic Field, Ismael L. Paiva, Yakir Aharonov, Jeff Tollaksen, Mordecai Waegell Apr 2020

Magnetic Forces In The Absence Of A Classical Magnetic Field, Ismael L. Paiva, Yakir Aharonov, Jeff Tollaksen, Mordecai Waegell

Mathematics, Physics, and Computer Science Faculty Articles and Research

It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine quantum systems in specially designed configurations. This generalizes a previous work where such energy barriers arose from flux lines with half-integer fluxons. Furthermore, it is shown how the Landau levels can be obtained from a two-dimensional grid of flux lines. These results suggest ...


The Breakup Of A Helium Cluster After Removing Attractive Interaction Among A Significant Number Of Atoms In The Cluster, Tao Pang Apr 2020

The Breakup Of A Helium Cluster After Removing Attractive Interaction Among A Significant Number Of Atoms In The Cluster, Tao Pang

Physics & Astronomy Faculty Publications

The breakup of a quantum liquid droplet is examined through a 4He cluster by removing the attractive tail in the interaction between some of the atoms in the system with the diffusion quantum Monte Carlo simulation. The ground-state energy, kinetic energy, cluster size, and density profile of the cluster are evaluated against the percentage of the atoms without the attractive tail. The condition for the cluster to lose its ability to form a quantum liquid droplet at zero temperature is found and analyzed. The cluster is no longer able to form a quantum liquid droplet when about two-thirds of pairs ...


Polarization Of Majorana Fermions In A Background Current, Lukas Karoly, David C. Latimer Jan 2020

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 ...


Optical-Depth Scaling Of Light Scattering From A Dense And Cold Atomic 87Rb Gas, K. J. Kemp, S. J. Roof, M. D. Havey, I. M. Sokolov, D. V. Kupriyanov, W. Guerin Jan 2020

Optical-Depth Scaling Of Light Scattering From A Dense And Cold Atomic 87Rb Gas, K. J. Kemp, S. J. Roof, M. D. Havey, I. M. Sokolov, D. V. Kupriyanov, W. Guerin

Physics Faculty Publications

We report investigation of near-resonance light scattering from a cold and dense atomic gas of 87Rb atoms. Measurements are made for probe frequencies tuned near the F=2→ F'=3 nearly closed hyperfine transition, with particular attention paid to the dependence of the scattered light intensity on detuning from resonance, the number of atoms in the sample, and atomic sample size. We find that, over a wide range of experimental variables, the optical depth of the atomic sample serves as an effective single scaling parameter which describes well all the experimental data.


Neutron Valence Structure From Nuclear Deep Inelastic Scattering, E. P. Segarra, A. Schmidt, T. Kutz, D. W. Higinbotham, E. Piasetzky, M. Strikman, L. B. Weinstein, O. Hen Jan 2020

Neutron Valence Structure From Nuclear Deep Inelastic Scattering, E. P. Segarra, A. Schmidt, T. Kutz, D. W. Higinbotham, E. Piasetzky, M. Strikman, L. B. Weinstein, O. Hen

Physics Faculty Publications

Mechanisms of spin-flavor SU(6) symmetry breaking in quantum chromodynamics (QCD) are studied via an extraction of the free neutron structure function from a global analysis of deep inelastic scattering (DIS) data on the proton and on nuclei from A = 2 (deuterium) to 208 (lead). Modification of the structure function of nucleons bound in atomic nuclei (known as the EMC effect) are consistently accounted for within the framework of a universal modification of nucleons in short-range correlated (SRC) pairs. Our extracted neutron-to-proton structure function ratio Fn2/Fp2 becomes constant for xB ≥ 0.6, equaling 0 ...


Intrinsic Transverse Momentum And Evolution In Weighted Spin Asymmetries, Jian-Wei Qiu, Ted C. Rogers, Bowen Wang Jan 2020

Intrinsic Transverse Momentum And Evolution In Weighted Spin Asymmetries, Jian-Wei Qiu, Ted C. Rogers, Bowen Wang

Physics Faculty Publications

The transverse momentum-dependent (TMD) and collinear higher twist theoretical factorization frameworks are the most frequently used approaches to describe spin-dependent hard cross sections weighted by and integrated over transverse momentum. Of particular interest is the contribution from small transverse momentum associated with the target bound state. In phenomenological applications, this contribution is often investigated using transverse momentum weighted integrals that sharply regulate the large transverse momentum contribution, for example, with Gaussian parametrizations. Since the result is a kind of hybrid of TMD and collinear (inclusive) treatments, it is important to establish if and how the formalisms are related in applications ...


B-Meson Light-Cone Distribution Amplitude From Euclidean Quantities, Wei Wang, Yu-Ming Wang, Ji Xu, Shuai Zhao Jan 2020

B-Meson Light-Cone Distribution Amplitude From Euclidean Quantities, Wei Wang, Yu-Ming Wang, Ji Xu, Shuai Zhao

Physics Faculty Publications

A new method for the model-independent determination of the light-cone distribution amplitude of the B-meson in heavy quark effective theory (HQET) is proposed by combining the large momentum effective theory and the numerical simulation technique on the Euclidean lattice. We demonstrate the autonomous scale dependence of the nonlocal quasi-HQET operator with the aid of the auxiliary field approach, and further determine the perturbative matching coefficient entering the hard-collinear factorization formula for the B-meson quasidistribution amplitude at the one-loop accuracy. These results will be crucial to explore the partonic structure of heavy-quark hadrons in the static limit and to ...


Measurement Of The ³He Spin-Structure Functions And Of Neutron (³He) Spin-Dependent Sum Rules At 0 .035≤Q²≤0 .24 Gev², V. Sulkosky, D. Hayes, C. E. Hyde, P. E. Ulmer, X. Zheng, L. Zhu, Et Al., Jefferson Lab E97-110 Collaboration Jan 2020

Measurement Of The ³He Spin-Structure Functions And Of Neutron (³He) Spin-Dependent Sum Rules At 0 .035≤Q²≤0 .24 Gev², V. Sulkosky, D. Hayes, C. E. Hyde, P. E. Ulmer, X. Zheng, L. Zhu, Et Al., Jefferson Lab E97-110 Collaboration

Physics Faculty Publications

The spin-structure functions g1 and g2, and the spin-dependent partial cross-section σπ have been extracted from the polarized cross-sections differences,

Δσ∥ (ν, Q2) and Δσ⊥ (ν,Q2) measured for the 3He(e, e')X reaction, in the E97-110 experiment at Jefferson Lab. Polarized electrons with energies from 1.147 to 4.404GeV were scattered at angles of 6and 9from a longitudinally or transversely polarized 3He target. The data cover the kinematic regions of the quasi-elastic, resonance production and beyond. From the extracted spin-structure functions, the first moments Γ1 ...


Gluon Pseudo-Distributions At Short Distances: Forward Case, Ian Balitsky, Wayne Morris, Anatoly Radyushkin Jan 2020

Gluon Pseudo-Distributions At Short Distances: Forward Case, Ian Balitsky, Wayne Morris, Anatoly Radyushkin

Physics Faculty Publications

We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the gluon PDF in the light-cone z2 → 0 limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources of the ln⁡(−z2)-dependence at short distances z2. The UV terms cancel in the reduced Ioffe-time distribution (ITD), and ...


Klf Analysis Report: Meson Spectroscopy Simulation Studies, Shankar Adhikari, Moskov Amaryan Jan 2020

Klf Analysis Report: Meson Spectroscopy Simulation Studies, Shankar Adhikari, Moskov Amaryan

Physics Faculty Publications

This analysis report is written as a supplemental for the strange meson spectroscopy part of the KLF proposal submitted to the JLab PAC48.


Developing A High Resolution Zdc For The Eic, J. H. Lee, T. Sako, K. Tanida, M. Murray, Q. Wang, N. Nickel, Y. Yamazaki, Y. Itow, H. Menjo, T. Shibata, C. E. Hyde, V. Baturin, Y. Goto, I. Nakagawa, R. Seidl, K. Kawade, A. Deshpande, B. Schmookler, K. Nakano, T. Chujo, Y. Miyachi Jan 2020

Developing A High Resolution Zdc For The Eic, J. H. Lee, T. Sako, K. Tanida, M. Murray, Q. Wang, N. Nickel, Y. Yamazaki, Y. Itow, H. Menjo, T. Shibata, C. E. Hyde, V. Baturin, Y. Goto, I. Nakagawa, R. Seidl, K. Kawade, A. Deshpande, B. Schmookler, K. Nakano, T. Chujo, Y. Miyachi

Physics Faculty Publications

The Electron Ion Collider offers the opportunity to make un-paralleled multidimen- sional measurements of the spin structure of the proton and nuclei, as well as a study of the onset of partonic saturation at small Bjorken-x [1]. An important requirement of the physics program is the tagging of spectator neutrons and the identification of forward photons. We propose to design and build a Zero Degree Calorimeter, or ZDC, to measure photons and neutrons with excellent energy & position resolution.


Optimizing Measurement Strengths For Qubit Quasiprobabilities Behind Out-Of-Time-Ordered Correlators, Razieh Mohseninia, José Raúl González Alonso, Justin Dressel Dec 2019

Optimizing Measurement Strengths For Qubit Quasiprobabilities Behind Out-Of-Time-Ordered Correlators, Razieh Mohseninia, José Raúl González Alonso, Justin Dressel

Mathematics, Physics, and Computer Science Faculty Articles and Research

Out-of-time-ordered correlators (OTOCs) have been proposed as a tool to witness quantum information scrambling in many-body system dynamics. These correlators can be understood as averages over nonclassical multitime quasiprobability distributions (QPDs). These QPDs have more information and their nonclassical features witness quantum information scrambling in a more nuanced way. However, their high dimensionality and nonclassicality make QPDs challenging to measure experimentally. We focus on the topical case of a many-qubit system and show how to obtain such a QPD in the laboratory using circuits with three and four sequential measurements. Averaging distinct values over the same measured distribution reveals either ...


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 Dec 2019

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 In0.52Al0.48As(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 ...


Parton Distribution Functions From Loffe Time Pseudo-Distributions, Bálint Joó, Joseph Karpie, Kostas Orginos, Anatoly V. Radyushkin, David Richards, Savvas Zafeiropoulos Dec 2019

Parton Distribution Functions From Loffe Time Pseudo-Distributions, Bálint Joó, Joseph Karpie, Kostas Orginos, Anatoly V. Radyushkin, David Richards, Savvas Zafeiropoulos

Physics Faculty Publications

In this paper, we present a detailed study of the unpolarized nucleon parton distribution function (PDF) employing the approach of parton pseudo-distribution functions. We perform a systematic analysis using three lattice ensembles at two volumes, with lattice spacings a = 0.127 fm and a = 0.094 fm, for a pion mass of roughly 400 MeV. With two lattice spacings and two volumes, both continuum limit and infinite volume extrapolation systematic errors of the PDF are considered. In addition to the x dependence of the PDF, we compute their first two moments and compare them with the pertinent phenomenological determinations.


Generalized Parton Distributions And Pseudodistributions, Anatoly V. Radyushkin Dec 2019

Generalized Parton Distributions And Pseudodistributions, Anatoly V. Radyushkin

Physics Faculty Publications

We derive one-loop matching relations for the Ioffe-time distributions (ITDs) related to the pion distribution amplitude (DA) and generalized parton distributions (GPDs). They are obtained from a universal expression for the one-loop correction in an operator form, and will be used in the ongoing lattice calculations of the pion DA and GPDs within the parton pseudodistributions approach.


Pion Valence Structure From Ioffe-Time Parton Pseudodistribution Functions, Bálint Joó, Joseph Karpie, Kostas Orinos, Anatoly V. Radyushkin, David G. Richards, Raza Sabbir Sufian, Savvas Zafeiropoulos Dec 2019

Pion Valence Structure From Ioffe-Time Parton Pseudodistribution Functions, Bálint Joó, Joseph Karpie, Kostas Orinos, Anatoly V. Radyushkin, David G. Richards, Raza Sabbir Sufian, Savvas Zafeiropoulos

Physics Faculty Publications

We present a calculation of the pion valence quark distribution extracted using the formalism of reduced Ioffe-time pseudodistributions or more commonly known as pseudo-PDFs. Our calculation is carried out on two different 2 + 1 flavor QCD ensembles using the isotropic-clover fermion action, with lattice dimensions 243 × 64 and 323 × 96 at the lattice spacing of a = 0.127 fm, and with the quark mass equivalent to a pion mass of mπ ≃ 415 MeV. We incorporate several combinations of smeared-point and smeared-smeared pion source-sink interpolation fields in obtaining the lattice QCD matrix elements using the summation method. After ...


Collinear Factorization In Wide-Angle Hadron Pair Production In E + E − Annihilation, E. Moffat, T. C. Rogers, N. Sato, A. Signori Nov 2019

Collinear Factorization In Wide-Angle Hadron Pair Production In E + E − Annihilation, E. Moffat, T. C. Rogers, N. Sato, A. Signori

Physics Faculty Publications

We compute the inclusive unpolarized dihadron production cross section in the far from back-to-back region of e+ e− annihilation in leading order pQCD using existing fragmentation function fits and standard collinear factorization, focusing on the large transverse momentum region where transverse momentum is comparable to the hard scale (the center-of-mass energy). We compare with standard transverse-momentum-dependent (TMD) fragmentation function-based predictions intended for the small transverse momentum region with the aim of testing the expectation that the two types of calculation roughly coincide at intermediate transverse momentum. We find significant tension, within the intermediate transverse momentum region, between calculations done with ...


Lorentz And Cpt Tests Using Penning Traps, Yunhua Ding Oct 2019

Lorentz And Cpt Tests Using Penning Traps, Yunhua Ding

Physics and Astronomy Faculty Publications

The theoretical prospects for quantum electrodynamics with Lorentz-violating operators of mass dimensions up to six are revisited in this work. The dominant effects due to Lorentz and CPT violation are studied in measurements of magnetic moments of particles confined in Penning traps. Using recently reported experimental results, new coefficients for Lorentz violation are constrained and existing bounds of various coefficients are improved.


Numerical Exploration Of Three Relativistic Particles In A Finite Volume Including Two-Particle Resonances And Bound States, Fernando Romero-López, Stephen R. Sharpe, Tyler D. Blanton, Raúl A. Briceño, Maxwell T. Hansen Oct 2019

Numerical Exploration Of Three Relativistic Particles In A Finite Volume Including Two-Particle Resonances And Bound States, Fernando Romero-López, Stephen R. Sharpe, Tyler D. Blanton, Raúl A. Briceño, Maxwell T. Hansen

Physics Faculty Publications

In this work, we use an extension of the quantization condition, given in ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the two-particle K matrix that required the absence of two-particle bound states or narrow two-particle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the K-matrix-like quantity that enters the quantization condition. With this in hand ...


Benchmarks Of Nonclassicality For Qubit Arrays, Mordecai Waegell, Justin Dressel Aug 2019

Benchmarks Of Nonclassicality For Qubit Arrays, Mordecai Waegell, Justin Dressel

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present a set of practical benchmarks for N-qubit arrays that economically test the fidelity of achieving multi-qubit nonclassicality. The benchmarks are measurable correlators similar to two-qubit Bell correlators, and are derived from a particular set of geometric structures from the N-qubit Pauli group. These structures prove the Greenberger–Horne–Zeilinger (GHZ) theorem, while the derived correlators witness genuine N-partite entanglement and establish a tight lower bound on the fidelity of particular stabilizer state preparations. The correlators need only MN + 1 distinct measurement settings, as opposed to the 22N − 1 settings that would normally be required ...


Stereodynamical Control Of A Quantum Scattering Resonance In Cold Molecular Collisions, Pablo G. Jambrina, James F.E. Croft, Hua Guo, Mark Brouard, Balakrishnan Naduvalath, F. Javier Aoiz Jul 2019

Stereodynamical Control Of A Quantum Scattering Resonance In Cold Molecular Collisions, Pablo G. Jambrina, James F.E. Croft, Hua Guo, Mark Brouard, Balakrishnan Naduvalath, F. Javier Aoiz

Chemistry and Biochemistry Faculty Publications

Cold collisions of light molecules are often dominated by a single partial wave resonance. For the rotational quenching of HD (v=1, j=2) by collisions with ground state para-H2, the process is dominated by a single L=2 partial wave resonance centered around 0.1 K. Here, we show that this resonance can be switched on or off simply by appropriate alignment of the HD rotational angular momentum relative to the initial velocity vector, thereby enabling complete control of the collision outcome.


Topological Nodal Line Semimetals In Graphene Network Structures, Jian-Tao Wang, Hongming Weng, Chengfeng Chen Jul 2019

Topological Nodal Line Semimetals In Graphene Network Structures, Jian-Tao Wang, Hongming Weng, Chengfeng Chen

Physics & Astronomy Faculty Publications

Topological semimetals are a fascinating class of quantum materials that possess extraordinary electronic and transport properties. These materials have attracted great interests in recent years for their fundamental significance and potential device applications. There have been intensive studies suggested that three-dimensional graphene networks support topological semimetals with two types of continuous nodal lines: one is to form closed nodal rings in Brillouin zone and the other ones traversing the whole Brillouin zone to be periodically connected. Carbon has negligible spin-orbit coupling, non-magnetism and great diversity of allotropes, which makes it very promising in realizing topological nodal line semimetals. Here we ...


Experimental Evidence Supportive Of The Quantum Dna Model, F. Matthew Mihelic May 2019

Experimental Evidence Supportive Of The Quantum Dna Model, F. Matthew Mihelic

Faculty Publications

The DNA molecule can be modeled as a quantum logic processor in which electron spin qubits are held coherently in each nucleotide in a logically and thermodynamically reversible enantiomeric symmetry, and can be coherently conducted along the pi-stacking interactions of aromatic nucleotide bases, while simultaneously being spin-filtered via the helicity of the DNA molecule. Entangled electron pairs can be separated by that spin-filtering, held coherently at biological temperatures in the topologically insulated nucleotide quantum gates, and incorporated into separate DNA strands during DNA replication. Two separate DNA strands that share quantum entangled electrons can be mitotically divided into individual cells ...


Free Electron Sources And Diffraction In Time, Eric R. Jones May 2019

Free Electron Sources And Diffraction In Time, Eric R. Jones

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

The quantum revolution of the last century advanced synergistically with technology, for example, with control of the temporal and spatial coherence, and the polarization state of light. Indeed, experimental confirmation of the quirks of quantum theory, as originally highlighted by Einstein, Podolsky, and Rosen, through Bohm, and then Bell, have been performed with photons, i.e., electromagnetic wave packets prepared in the same quantum states. Experimental tests of quantum mechanics with matter wave packets have been limited due to challenges in preparing all of the packets with similar quantum states. While great strides have been made for trapped atoms and ...


Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert May 2019

Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert

Dissertations, Theses, and Student Research Papers in Mathematics

This dissertation investigates the properties of unbounded derivations on C*-algebras, namely the density of their analytic vectors and a property we refer to as "kernel stabilization." We focus on a weakly-defined derivation δD which formalizes commutators involving unbounded self-adjoint operators on a Hilbert space. These commutators naturally arise in quantum mechanics, as we briefly describe in the introduction.

A first application of kernel stabilization for δD shows that a large class of abstract derivations on unbounded C*-algebras, defined by O. Bratteli and D. Robinson, also have kernel stabilization. A second application of kernel stabilization provides a ...