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Articles 31 - 60 of 558

Full-Text Articles in Physics

Using Digital Holographic Microscopy To Characterize Vibrio's Chemotaxis, Jacqueline Acres, Eric Valentino May 2022

Using Digital Holographic Microscopy To Characterize Vibrio's Chemotaxis, Jacqueline Acres, Eric Valentino

Student Research Symposium

Vibrio alginolyticus is a marine bacterium that displays distinctive chemotactic behavior. Chemotaxis is the ability to move in response to a concentration gradient, either in the direction of nutrients or away from repellants. Vibrio's single, polar flagellum allows it to form a tight cloud in the presence of a chemoattractant. In this work, we experimentally characterize cloud sizes after both normal culture conditions and simulated microgravity using digital holographic microscopy or DHM. DHM allows visualization of volumetric samples by recording x,y,z and t information in holograms. Plane-by-plane reconstruction retrieves the z-plane information which can then by stitched together into hyperstacks …


Surface Plasmon Characterization In Ag Nanotriangles For Evaluation Of Fano Resonance Conditions, Nabila Islam May 2022

Surface Plasmon Characterization In Ag Nanotriangles For Evaluation Of Fano Resonance Conditions, Nabila Islam

Student Research Symposium

Surface plasmon polariton (SPP) is a collective oscillation of electrons and light at the metal -dielectric interface excited by the incident radiation on metal surface through the momentum matching conditions. The properties of SPPs and the resonance conditions are highly dependent on the confining materials and geometry of the confining nanostructure. The sensitivity of the surface plasmon resonance to the property of the confining materials made Surface plasmon resonance (SPR) sensors a central tool for biosensing. However, the frequency resolution of SPR sensors is typically limited by the broad resonance of the SPR mode. The resolution can be enhanced through …


Objective Crystallographic Symmetry Classifications Of A Noisy Crystal Pattern With Strong Fedorov-Type Pseudo­Symmetries And Its Optimal Image-Quality Enhancement, Peter Moeck May 2022

Objective Crystallographic Symmetry Classifications Of A Noisy Crystal Pattern With Strong Fedorov-Type Pseudo­Symmetries And Its Optimal Image-Quality Enhancement, Peter Moeck

Physics Faculty Publications and Presentations

Statistically sound crystallographic symmetry classifications are obtained with information-theory-based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic patterns with strong Fedorov-type pseudo­symmetries and varying amounts of noise serve as examples. Contrary to traditional crystallographic symmetry classifications with an image processing program such as CRISP, the classification process does not need to be supervised by a human being and is free of any subjectively set thresholds in the geometric model selection process. This enables crystallographic symmetry classification of digital images that are more or less periodic in two dimensions (2D), also known as crystal …


Quantification Of Motility In Bacillus Subtilis At Temperatures Up To 84°C Using A Submersible Volumetric Microscope And Automated Tracking, Megan M. Dubay, Nikki Johnston, Mark Wronkiewicz, Jake Lee, Chris Lindensmith, Jay Nadeau Apr 2022

Quantification Of Motility In Bacillus Subtilis At Temperatures Up To 84°C Using A Submersible Volumetric Microscope And Automated Tracking, Megan M. Dubay, Nikki Johnston, Mark Wronkiewicz, Jake Lee, Chris Lindensmith, Jay Nadeau

Physics Faculty Publications and Presentations

We describe a system for high-temperature investigations of bacterial motility using a digital holographic microscope completely submerged in heated water. Temperatures above 90°C could be achieved, with a constant 5°C offset between the sample temperature and the surrounding water bath. Using this system, we observed active motility in Bacillus subtilis up to 66°C. As temperatures rose, most cells became immobilized on the surface, but a fraction of cells remained highly motile at distances of >100 μm above the surface. Suspended non-motile cells showed Brownian motion that scaled consistently with temperature and viscosity. A novel open-source automated tracking package was used …


Characterization Of High Mobility Channels For Use In Quantum Computing Devices, Payam Amin Mar 2022

Characterization Of High Mobility Channels For Use In Quantum Computing Devices, Payam Amin

Dissertations and Theses

Quantum computing promises computation that is fundamentally beyond the reach of classical computers. For the realization of a full-scale quantum computer, millions of quantum bits need to be fabricated on an integrated circuit and operated at cryogenic temperatures. Silicon and silicon-germanium based electron spin quantum bits have the advantage of leveraging decades of semiconductor industry knowledge for high volume manufacturability.

During the process development of any semiconductor device, material characterization is essential to understand and improve the process. Transmission electron microscopy is the only technique that could offer localized high spatial resolution characterization. In this work we have introduced two …


Effects Of Pore-Forming Peptides (Melittin And Magainin 2) On The Phospholipid Bilayer Interior, Elmukhtar Ehmed Alhatmi Mar 2022

Effects Of Pore-Forming Peptides (Melittin And Magainin 2) On The Phospholipid Bilayer Interior, Elmukhtar Ehmed Alhatmi

Dissertations and Theses

Antimicrobial peptides (AMPs) are one of the most promising solutions to drug-resistant bacteria. Melittin and magainin 2 are two of the most representative and extensively studied AMPs. In this research, I investigated the interaction of these two AMPs with three models of cell membranes: 80% POPC 20% POPG, 40%POPC 40% POPE and 20% POPG, and 80%POPC 20%POPG plus 30% mole fraction of cholesterol. Time-resolved fluorescence emission and fluorescence anisotropy decays of the fluorescent probe 1,6-diphenyl-1,3,5-hexatriene (DPH) were analyzed to determine the effects of AMPs on the bilayer headgroup packing and changes in the interior of the phospholipid bilayer during the …


Maximum Entropy And Constraints In Composite Systems, John D. Ramshaw Feb 2022

Maximum Entropy And Constraints In Composite Systems, John D. Ramshaw

Physics Faculty Publications and Presentations

The principle of maximum entropy (PME), as expounded by Jaynes, is based on the maximization of the Boltzmann-Gibbs-Shannon (BGS) entropy subject to linear constraints. The resulting probability distributions are of canonical (exponential) form. However, the rationale for linear constraints is nebulous, and probability distributions are not always canonical. Here we show that the correct noncanonical distribution for a system in equilibrium with a finite heat bath is implied by the unconstrained maximization of the total BGS entropy of the system and bath together. This procedure is shown to be equivalent to maximizing the BGS entropy of the system alone subject …


Quantum Field Theories, Topological Materials, And Topological Quantum Computing, Muhammad Ilyas Dec 2021

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 …


2d Vs 3d Tracking In Bacterial Motility Analysis, Jacqueline Acres, Jay Nadeau Dec 2021

2d Vs 3d Tracking In Bacterial Motility Analysis, Jacqueline Acres, Jay Nadeau

Physics Faculty Publications and Presentations

Digital holographic microscopy provides the ability to observe throughout a large volume without refocusing. This capability enables simultaneous observations of large numbers of microorganisms swimming in an essentially unconstrained fashion. However, computational tools for tracking large 4D datasets remain lacking. In this paper, we examine the errors introduced by tracking bacterial motion as 2D projections vs. 3D volumes under different circumstances: bacteria free in liquid media and bacteria near a glass surface. We find that while XYZ speeds are generally equal to or larger than XY speeds, they are still within empirical uncertainties. Additionally, when studying dynamic surface behavior, the …


The Return To Anisotropy Across A Jet In Crossflow, Gregory P. Sakradse Sep 2021

The Return To Anisotropy Across A Jet In Crossflow, Gregory P. Sakradse

Dissertations and Theses

With data from experiments on a jet of air emitting from an orifice flush with the floor of a wind tunnel providing a transverse flow, analysis is conducted to extract information about the state of anisotropy in the Reynolds stress tensor. Inflow velocities are modulated across two distinct turbulence intensity regimes while holding jet exit conditions constant, providing an opportunity to isolate effects of both jet to crossflow velocity ratio, r and the effects of the turbulence carried by the crossflow. Anisotropy in the Reynolds stress tensor is examined through anisotropy invariant maps and evolution of the function F, …


Efficient Neuromorphic Algorithms For Gamma-Ray Spectrum Denoising And Radionuclide Identification, Merlin Phillip Carson Sep 2021

Efficient Neuromorphic Algorithms For Gamma-Ray Spectrum Denoising And Radionuclide Identification, Merlin Phillip Carson

Dissertations and Theses

Radionuclide detection and identification are important tasks for deterring a potentially catastrophic nuclear event. Due to high levels of background radiation from both terrestrial and extraterrestrial sources, some form of noise reduction pre-processing is required for a gamma-ray spectrum prior to being analyzed by an identification algorithm so as to determine the identity of anomalous sources. This research focuses on the use of neuromorphic algorithms for the purpose of developing low power, accurate radionuclide identification devices that can filter out non-anomalous background radiation and other artifacts created by gamma-ray detector measurement equipment, along with identifying clandestine, radioactive material.

A sparse …


Investigation Of Environmental-Friendly, Membraneless Hydrogen Peroxide Fuel Cells, Bao Nguyen Aug 2021

Investigation Of Environmental-Friendly, Membraneless Hydrogen Peroxide Fuel Cells, Bao Nguyen

Dissertations and Theses

Human-induced climate change is one of the biggest threats to humanity in the 21st century. This is caused by the increase in greenhouse gas concentrations in the Earth's atmosphere. The burning of fossil fuels is the primary cause of climate change. This problem can be addressed by replacing fossil fuels with fuel sources that have clean by-products and are cost-effective. For the last few decades, hydrogen (H2) has been extensively studied as an alternative to carbon-based fossil fuels. Currently, H2 still has many shortcomings for commercial applications. The photocatalytic production of H2 still suffers from …


Proximal Policy Optimization For Radiation Source Search, Philippe Erol Proctor Aug 2021

Proximal Policy Optimization For Radiation Source Search, Philippe Erol Proctor

Dissertations and Theses

Rapid localization and search for lost nuclear sources in a given area of interest is an important task for the safety of society and the reduction of human harm. Detection, localization and identification are based upon the measured gamma radiation spectrum from a radiation detector. The nonlinear relationship of electromagnetic wave propagation paired with the probabilistic nature of gamma ray emission and background radiation from the environment leads to ambiguity in the estimation of a source's location. In the case of a single mobile detector, there are numerous challenges to overcome such as weak source activity, multiple sources, or the …


Microscopic Object Classification Through Passive Motion Observations With Holographic Microscopy, Christian Lindensmith, Jay Nadeau, Manuel Bedrossian, Louis Sumrall, J. Kent Wallace, Eugene Serabyn Aug 2021

Microscopic Object Classification Through Passive Motion Observations With Holographic Microscopy, Christian Lindensmith, Jay Nadeau, Manuel Bedrossian, Louis Sumrall, J. Kent Wallace, Eugene Serabyn

Physics Faculty Publications and Presentations

Digital holographic microscopy provides the ability to observe throughout a volume that is large compared to its resolution element without the need to refocus through the volume. This capability enables simultaneous observations of large numbers of small objects within such a volume. We have constructed a microscope that can observe a volume 0.4 x 0.4 x 1.0 μm with submicrometer resolution for observation of microorganisms and minerals in liquid environments in earth and on potential planetary missions. Because environmental samples are likely to contain mixtures of inorganics and microorganisms that are of comparable sizes near the resolution limit of the …


Simulation Of Light Propagation Captured By Photoemission Electron Microscopy (Peem), Nabila Islam Jul 2021

Simulation Of Light Propagation Captured By Photoemission Electron Microscopy (Peem), Nabila Islam

Dissertations and Theses

The Photoemission electron microscopes (PEEM) is a powerful tool capable of synchronously imaging wave nature of light manifested by interference patterns as well as its particle nature through the energy exchange between the incident photons and the photoemitted imaging electrons. PEEM offers a non-invasive high-resolution approach for studying light propagation and interaction phenomena within a nanophotonic waveguide [7,8]. The electric field intensity variation of the interference pattern yielded by the interaction between the incident light and the guided mode coupled into the waveguide produces varying photoemission yields creating contrast in PEEM image. The guided modes cannot be excited simply by …


Self-Contained Photon Coincidence Counting With Ni Myrio Ecosystem, Georges Oates Larsen, Andres H. La Rosa Jun 2021

Self-Contained Photon Coincidence Counting With Ni Myrio Ecosystem, Georges Oates Larsen, Andres H. La Rosa

University Honors Theses

Digital coincidence counting units (CCU) have made experimental verification of fundamental quantum mechanical principles financially accessible to undergraduate level teaching programs. However, recent implementations of these systems are not easily ported to National Instruments (NI) FPGAs, making them unsuitable for physics departments that have heavily invested in the NI ecosystem. Therefore, there is clear need for a detailed implementation based on an NI FPGA. We present a formal description of one such implementation, based on the NI myRIO (NI's lower-cost, student-oriented offering) which achieves 6.9 ns minimum guaranteed-distinguishable delay and 32.2 MHz peak coincidence counting rate with four input channels …


Photoemission Electron Microscopy For Direct Observation Of Photonic And Plasmonic Phenomena, Theodore Stenmark May 2021

Photoemission Electron Microscopy For Direct Observation Of Photonic And Plasmonic Phenomena, Theodore Stenmark

Dissertations and Theses

Photoemission electron microscopy (PEEM) is a high-resolution microscopy technique that collects photoemitted electrons from the sample surface to form an image. PEEM offers a non-scanning imaging method with a spatial resolution in the range of 5-100nm by combining the advantages of light excitation and electron imaging. Our work looks at PEEM as an analysis tool for photonic and plasmonic phenomena. Photonic wave guiding structures exhibiting a strong dispersion relation have attracted considerable attention for applications in integrated optics, communications and sensing devices. Line defects in a photonic crystal (PC) slab offer a highly efficient way to create light with group …


Dipole Emission Characteristics Near A Topological Insulator Sphere Coated With A Metallic Nanoshell, Huai-Yi Xie, Railing Chang, P. T. Leung Apr 2021

Dipole Emission Characteristics Near A Topological Insulator Sphere Coated With A Metallic Nanoshell, Huai-Yi Xie, Railing Chang, P. T. Leung

Physics Faculty Publications and Presentations

Topological insulators (TI) are quantum states of (2D/3D) matter with an insulating interior but conducting edge/surface states, with these boundary conducting states being protected topologically by time-reversal symmetry. Composite materials of heavy atoms such as Bi2Te3 can be fabricated to show TI properties due to the strong intrinsic spin-orbit coupling of the electrons in these materials. Among the so many intriguing physical properties of these materials, their topological magneto-electric (TME) response is unique and has been studied intensively in the literature, leading to intriguing optical effects such as Faraday and Kerr rotations of incident polarized beams at …


Quantifying Biotic Voc Emissions From Moss: Air Quality Impacts Of Isoprene And Monoterpenes In Urban Environments, Danlyn L. Brennan Apr 2021

Quantifying Biotic Voc Emissions From Moss: Air Quality Impacts Of Isoprene And Monoterpenes In Urban Environments, Danlyn L. Brennan

University Honors Theses

Plant-derived biogenic volatile organic compound (VOC) emissions contribute to secondary emissions of molecules such as ground-level ozone (O3) and PM 2.5 which are known to be harmful to the environment and negatively impact human health. Currently, the most known biogenic VOC emissions are from vascular plants like trees and economically significant crops. Air quality models use known emission rates from these measurements and have many unknown sources yet to identify. Unknown values of emissions occur due to a lack of measurements of a wider variety of plants, especially that of smaller and lesser-studied species of bryophytes; mosses. This …


Complex Fluid Dynamics: Chemo-Hydrodynamics Driven By Autocatalytic Reaction Fronts, Matthew Walter Eskew Mar 2021

Complex Fluid Dynamics: Chemo-Hydrodynamics Driven By Autocatalytic Reaction Fronts, Matthew Walter Eskew

Dissertations and Theses

Chemo-hydrodynamics generated from reaction-diffusion-convection processes of autocatalytic chemical systems are extensively studied for their applications in modeling complex systems. Compared to the more extensively studied autocatalytic systems, chlorite-tetrathionate and chlorite-trithionate, the chlorite-thiourea systems is relatively unexplored. Compared to the two previous systems, chlorite-thiourea has more straightforward chemical kinetics. To narrow the gap between chlorite-thiourea and the other systems a combination of experimental study and numerical simulation were employed to quantify this system.

Compared to established literature, experiments were performed at five orders of magnitude lower concentration of indicator, minimizing confounding effects of indicator on hydrodynamic motion. To accurately image the …


The Influence Of Spaceflight And Simulated Microgravity On Bacterial Motility And Chemotaxis, Jacqueline Acres, Myka Jaap Youngapelian, Jay Nadeau Feb 2021

The Influence Of Spaceflight And Simulated Microgravity On Bacterial Motility And Chemotaxis, Jacqueline Acres, Myka Jaap Youngapelian, Jay Nadeau

Physics Faculty Publications and Presentations

As interest in space exploration rises, there is a growing need to quantify the impact of microgravity on the growth, survival, and adaptation of microorganisms, including those responsible for astronaut illness. Motility is a key microbial behavior that plays important roles in nutrient assimilation, tissue localization and invasion, pathogenicity, biofilm formation, and ultimately survival. Very few studies have specifically looked at the effects of microgravity on the phenotypes of microbial motility. However, genomic and transcriptomic studies give a broad general picture of overall gene expression that can be used to predict motility phenotypes based upon selected genes, such as those …


Using The Gouy Phase Anomaly To Localize And Track Bacteria In Digital Holographic Microscopy 4d Images, True Gibson, Manuel Bedrossian, Eugene Serabyn, Chris Lindensmith, Jay Nadeau Feb 2021

Using The Gouy Phase Anomaly To Localize And Track Bacteria In Digital Holographic Microscopy 4d Images, True Gibson, Manuel Bedrossian, Eugene Serabyn, Chris Lindensmith, Jay Nadeau

Physics Faculty Publications and Presentations

Described over 100 years ago, the Gouy phase anomaly refers to the additional π phase shift that is accumulated as a wave passes through focus. It is potentially useful in analyzing any type of phase-sensitive imaging; in light microscopy, digital holographic microscopy (DHM) provides phase information in the encoded hologram. One limitation of DHM is the weak contrast generated by many biological cells, especially unpigmented bacteria. We demonstrate here that the Gouy phase anomaly may be detected directly in the phase image using the z-derivative of the phase, allowing for precise localization of unlabeled, micrometer-sized bacteria. The use of dyes …


Investigation Of Prussian Blue Analogues As Cathode Materials For Next Generation Batteries, Neal Walters Kuperman Nov 2020

Investigation Of Prussian Blue Analogues As Cathode Materials For Next Generation Batteries, Neal Walters Kuperman

Dissertations and Theses

Since the beginning of the industrial revolution, the average global temperature has risen about 1 °C due increases in anthropogenic greenhouse gases emitted into the atmosphere. Of all human produced greenhouse gases, carbon dioxide is the most prevalent, with the production of electricity from fossil fuels being the major contributor.

Solar and wind power are promising net zero emission energy sources but only accounted for ~5% of global electricity generation in 2016. The most significant hurdle hindering their widespread adoption is the intermittent nature of the electricity generation. To overcome this limitation, significant resources need to be put into the …


The Gauge Principle From The Schrodinger-Born Wave Mechanics, P. T. Leung Nov 2020

The Gauge Principle From The Schrodinger-Born Wave Mechanics, P. T. Leung

Physics Faculty Publications and Presentations

We propose an elementary way of introducing the gauge principle to beginners with a background in only mechanics, electromagnetism, and quantum mechanics. This evolves from an apparent conflict in the Schrodinger-Born formulation of wave mechanics, and does not have to resort to advanced concepts like covariant derivative and minimal coupling. With such an approach, one would have appreciated how interactions can be dictated from consideration of internal symmetry of a physical system, which serves as a principle underlying the foundation of almost all modern physics. In addition, the gauge principle also serves as a resource providing consistency between the Born …


Genetically Encoded Phase Contrast Agents For Digital Holographic Microscopy, Arash Farhadi, Manuel Bedrossian, Justin Lee, Gabrielle H. Ho, Mikhail G. Shapiro, Jay Nadeau Oct 2020

Genetically Encoded Phase Contrast Agents For Digital Holographic Microscopy, Arash Farhadi, Manuel Bedrossian, Justin Lee, Gabrielle H. Ho, Mikhail G. Shapiro, Jay Nadeau

Physics Faculty Publications and Presentations

Quantitative phase imaging and digital holographic microscopy have shown great promise for visualizing the motion, structure and physiology of microorganisms and mammalian cells in three dimensions. However, these imaging techniques currently lack molecular contrast agents analogous to the fluorescent dyes and proteins that have revolutionized fluorescence microscopy. Here we introduce the first genetically encodable phase contrast agents based on gas vesicles. The relatively low index of refraction of the air-filled core of gas vesicles results in optical phase advancement relative to aqueous media, making them a “positive” phase contrast agent easily distinguished from organelles, dyes, or microminerals. We demonstrate this …


Investigation Of Magnetism In Transition Metal Chalcogenide Thin Films, Michael Adventure Hopkins Sep 2020

Investigation Of Magnetism In Transition Metal Chalcogenide Thin Films, Michael Adventure Hopkins

Dissertations and Theses

Layered two dimensional films have been a topic of interest in the materials science community driven by the intriguing properties demonstrated in graphene. Tunable layer dependent electrical and magnetic properties have been shown in these materials and the ability to grow in the hexagonal phase provides opportunities to grow isostructural stacked heterostructures. In this investigation, cobalt selenide (CoSe) and nickel selenide (NiSe) were grown in the hexagonal phase, which consist of central metal atoms that are natively ferromagnetic in bulk, hence providing the potential for interesting magnetic phases in thin film arrangements as well. These structures may play a role …


Electromagnetic Reciprocity In The Presence Of Topological Insulators, Huai-Yi Xie, P. T. Leung Sep 2020

Electromagnetic Reciprocity In The Presence Of Topological Insulators, Huai-Yi Xie, P. T. Leung

Physics Faculty Publications and Presentations

Electromagnetic reciprocity is studied in the presence of topological insulators (TI) with application of axion electrodynamics for harmonic electromagnetic fields. The corresponding generalized Lorentz and Feld-Tai type lemmas are derived in terms of the axion coupling parameter, and their correlation to the conditional symmetry in source-observer coordinates for the various Green dyadics is established subjected to different types of boundary conditions. Possible application of the results to the probing of the topological magneto-electric effects from TI is discussed.


Reducing A Class Of Two-Dimensional Integrals To One-Dimension With An Application To Gaussian Transforms, Jack C. Straton Sep 2020

Reducing A Class Of Two-Dimensional Integrals To One-Dimension With An Application To Gaussian Transforms, Jack C. Straton

Physics Faculty Publications and Presentations

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers multiplied by an arbitrary function of xy/ (x + y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.


Numerical Model Of A Radio Frequency Ion Source For Fusion Plasma Using Particle-In-Cell And Finite Difference Time Domain, Augustin L. Griswold Aug 2020

Numerical Model Of A Radio Frequency Ion Source For Fusion Plasma Using Particle-In-Cell And Finite Difference Time Domain, Augustin L. Griswold

University Honors Theses

Radio frequency (RF) plasma sources are common tool for application and study, and of particular interest for inertial electrostatic (IEC) fusion. Computational analysis is often carried out using particle in cell (PIC) methods or finite difference time domain (FDTD). However, a more holistic analysis is necessary as the particle distribution is highly dependant on the fields created by the plasma source. Herein, an analysis of a particular planar RF electrode with deuterium gas is provided which covers the fields and the particle behaviour using first FDTD then PIC. Further applications are discussed as well as further directions for this study.


A New Look At The Quantum Liouville Theorem, P. T. Leung, G. I. Ni Aug 2020

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.