Optimum quantization in dynamic systems.
Criterion for optimum design of quantizer imbedded in closed loop dynamic system is optimization of overall system performance expressed by variational criterion
QUANTIZER↗
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Optimum quantization in dynamic systems.
Quantizer optimal design for closed-loop dynamic and open-loop static systems
OPTIMIZATION↗
Quantized Grain Boundary States Promote Nanoparticle Alignment During Imperfect Oriented Attachment
Oriented attachment (OA) has become a well-recognized mechanism for the growth of metal, ceramic, and biomineral crystals. While many computational and experimental studies of OA have shown that particles can attach with some misorientation then rotate to remove adjoining grain boundaries, the underlying atomistic pathways for this “Imperfect OA” process remain the subject of debate. In this paper, molecular dynamics and in situ TEM were used to probe the crystallographic evolution of up to 30 gold and copper nanoparticles during aggregation. It was found that Imperfect OA occurs because (1) grain boundaries become quantized when their size is comparable to the separation between constituent dislocations and (2) kinetic barriers associated with the glide of grain boundary dislocations are small. In support of these findings, TEM experiments show the formation of a single crystal aggregate after annealing 9 initially misoriented, agglomerated particles with evidence of dislocation slip and twin formation during particle/grain alignment. These observations motivate future work on assembled nanocrystals with tailored defects and call for a revision of Read-Shockley models for grain boundary energies in nanocrystalline materials.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Exact quantization and analytic continuation
In this paper we give a streamlined derivation of the exact quantization condition (EQC) on the quantum periods of the Schrödinger problem in one dimension with a general polynomial potential, based on Wronskian relations. We further generalize the EQC to potentials with a regular singularity, describing spherical symmetric quantum mechanical systems in a given angular momentum sector. We show that the thermodynamic Bethe ansatz (TBA) equations that govern the quantum periods undergo nontrivial monodromies as the angular momentum is analytically continued between integer values in the complex plane. The TBA equations together with the EQC are checked numerically against Hamiltonian truncation at real angular momenta and couplings, and are used to explore the analytic continuation of the spectrum on the complex angular momentum plane in examples.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Coulomb branch quantization and abelianized monopole bubbling
We develop an approach to the study of Coulomb branch operators in 3D N = 4 gauge theories and the associated quantization structure of their Coulomb branches. This structure is encoded in a one-dimensional TQFT subsector of the full 3D theory, which we describe by combining several techniques and ideas. The answer takes the form of an associative and noncommutative star product algebra on the Coulomb branch. For “good” and “ugly” theories (according to the Gaiotto-Witten classification), we also exhibit a trace map on this algebra, which allows for the computation of correlation functions and, in particular, guarantees that the star product satisfies a truncation condition. This work extends previous work on abelian theories to the non-abelian case by quantifying the monopole bubbling that describes screening of GNO boundary conditions. In our approach, monopole bubbling is determined from the algebraic consistency of the OPE. This also yields a physical proof of the Bullimore-Dimofte-Gaiotto abelianization description of the Coulomb branch.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Nonperturbative matching between equal-time and lightcone quantization
We investigate the nonperturbative relation between lightcone (LC) and standard equal-time (ET) quantization in the context of λΦ4 theory in d = 2. We discuss the perturbative matching between bare parameters and the failure of its naive nonperturbative extension. We argue that they are nevertheless the same theory nonperturbatively, and that furthermore the nonperturbative map between bare parameters can be extracted from ET perturbation theory via Borel resummation of the mass gap. We test this map by using it to compare physical quantities computed using numerical Hamiltonian truncation methods in ET and LC.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Axion-gauge coupling quantization with a twist
The possible couplings of an axion to gauge fields depend on the global structure of the gauge group. If the Standard Model gauge group is minimal, or equivalently if fractionally charged color-singlet particles are forbidden, then the QCD axion’s Chern-Simons couplings to photons and gluons obey correlated quantization conditions. Specifically, the photon coupling can have a fractional part which is a multiple of 1/3, but which is determined by the gluon coupling. A consequence of this result is that, among all theories with a minimal gauge group and minimal axion coupling to gluons, the smallest possible axion-photon amplitude |g aγγ | arises for E/N = 8/3. This provides a new motivation for experiments targeting this axion-photon coupling.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Basis Light-Front Quantization: Recent Progress and Future Prospects
Light-front Hamiltonian field theory has advanced to the stage of becoming a viable non-perturbative method for solving forefront problems in strong interaction physics. Physics drivers include hadron mass spectroscopy, generalized parton distribution functions, spin structures of the hadrons, inelastic structure functions, hadronization, particle production by strong external time-dependent fields in relativistic heavy ion collisions, and many more. We review selected recent results and future prospects with basis light-front quantization that include fermion-antifermion bound states in QCD, fermion motion in a strong time-dependent external field and a novel non-perturbative renormalization scheme.
Physics↗
First quantized electrodynamics
The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation of electrons entangled in space or time. The parametrized formalism leads directly and without further conjecture to the Bethe–Salpeter equation for bound states. The formalism also yields the Uehling shift of the hydrogenic spectrum, the anomalous magnetic moment of the electron to leading order in the fine structure constant, the Lamb shift and the axial anomaly of QED. -- Highlights: •First-quantized electrodynamics of the parametrized Dirac equation is developed. •Unrestricted entanglement in time is made explicit. •Bethe and Salpeter’s equation for relativistic bound states is derived without further conjecture. •One-loop scattering corrections and the axial anomaly are derived using a partial summation. •Wide utility of semi-classical Quantum Electrodynamics is argued.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Investigation of process history and underlying phenomena associated with the synthesis of plutonium oxides using Vector Quantizing Variational Autoencoder
Accurate, high throughput, and unbiased analysis of plutonium oxide particles is needed for analysis of the phenomenology associated with process parameters in their synthesis. Compared to qualitative and taxonomic descriptors, quantitative descriptors of particle morphology through scanning electron microscopy (SEM) have shown success in analyzing process parameters of uranium oxides. Among other candidates, a neural network called a Vector Quantizing Variational Autoencoder (VQ-VAE) has shown the ability to quantitatively describe particle morphology to attain >85% accuracy in identifying uranium oxide processing routes. We utilize a VQ-VAE to quantitatively describe plutonium dioxide (PuO 2 ) particles created in a designed experiment and investigate their phenomenology and prediction of their process parameters. PuO 2 was calcined from Pu(III) oxalates that were precipitated under varying synthetic conditions that related to concentrations, temperature, addition and digestion times, precipitant feed, and strike order; the surface morphology of the resulting PuO 2 powders were analyzed by SEM. A pipeline was developed to extract and quantify useful image representations for individual particles with the VQ-VAE, then further reduce the dimensionality of the feature space using a bottlenecking neural network fit to perform multiple classification tasks simultaneously. The reduced feature space could predict process parameters with greater than 80% accuracies for some parameters with a single particle. They also showed utility for grouping particles with similar surface morphology characteristics together. Both the clustering and classification results reveal valuable information regarding which chemical process parameters chiefly influence the PuO 2 particle morphologies: strike order and oxalic acid feedstock. Doing the same analysis with multiple particles was shown to improve the classification accuracy on each process parameter over the use of a single particle, with statistically significant results generally seen with as few as four particles in a sample.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Optical phonons in nanostructured thin films composed by zincblende zinc selenide quantum dots in strong size-quantization regime: Competition between phonon confinement and strain-related effects
Raman scattering in combination with optical spectroscopy and structural studies by X-ray diffraction was employed to investigate the phonon confinement and strain-induced effects in 3D assemblies of variable-size zincblende ZnSe quantum dots close packed in thin film form. Nanostructured thin films were synthesized by colloidal chemical approach, while tuning of the nanocrystal size was enabled by post-deposition thermal annealing treatment. In-depth insights into the factors governing the observed trends of the position and half-width of the 1LO band as a function of the average QD size were gained. The overall shifts in the position of 1LO band were found to result from an intricate compromise between the influence of phonon confinement and lattice strain-induced effects. Both contributions were quantitatively and exactly modeled. Accurate assignments of the bands due to surface optical (SO) modes as well as of the theoretically forbidden transverse optical (TO) modes were provided, on the basis of reliable physical models (such as the dielectric continuum model of Ruppin and Englman). The size-dependence of the ratio of intensities of the TO and LO modes was studied and discussed as well. Relaxation time characterizing the phonon decay processes in as-deposited samples was found to be approximately 0.38 ps, while upon post-deposition annealing already at 200 °C it increases to about 0.50 ps. Both of these values are, however, significantly smaller than those characteristic for a macrocrystalline ZnSe sample. - Graphical abstract: Optical phonons in nanostructured thin films composed by zincblende zinc selenide quantum dots in strong size-quantization regime: competition between phonon confinement and strain-related effects. - Highlights: • Phonon confinement vs. strain-induced effects in ZnSe 3D QD assemblies were studied. • Shifts of the 1LO band result from an intricate compromise between the two effects. • SO and theoretically forbidden TO modes were accurately assigned. • Phonon relaxation time in as-deposited and annealed samples is 0.38 ps and 0.50 ps. • Both values are significantly smaller than in macrocrystalline ZnSe sample.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Finite-volume quantization condition from the N/D representation
We propose a new model-independent method for determining hadronic resonances from lattice QCD. The formalism is derived from the general principles of unitarity and analyticity, as encoded in the N/D representation of a partial-wave two-body amplitude. The associated quantization condition relates the finite-volume spectrum to the infinite-volume numerator $\mathscr{N}$, used to reconstruct the scattering amplitude from dispersive relations. Unlike the original Lüscher condition, this new formalism is valid for energies coinciding with the left-hand cuts from arbitrary one- and multiparticle exchanges.
Dawid, Sebastian M. [Univ. of Washington, Seattle,↗
The classical equations of motion of quantized gauge theories, Part 2: Electromagnetism
In this and companion papers, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the quantization of electromagnetism permits the existence of classical electric field states that do not obey Gauss’s law. These states are gauge invariant and their time evolution can be consistently described using the Schrödinger equation. The time evolution of these states is such that at the classical level, the full set of Maxwell’s equations would appear to hold, with the physical effects of these states being attributable to an auxiliary, static “shadow” charge density with no internal degrees of freedom. This density could affect the dynamics of charged particles in our universe and it may thus be of observational interest.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Combination of Cation Exchange and Quantized Ostwald Ripening for Controlling Size Distribution of Lead Chalcogenide Quantum Dots
A new strategy for narrowing the size distribution of colloidal quantum dots (QDs) was developed by combining cation exchange and quantized Ostwald ripening. Medium-sized reactant CdS(e) QDs were subjected to cation exchange to form the target PbS(e) QDs, and then small reactant CdS(e) QDs were added which were converted to small PbS(e) dots via cation exchange. The small-sized ensemble of PbS(e) QDs dissolved completely rapidly and released a large amount of monomers, promoting the growth and size-focusing of the medium-sized ensemble of PbS(e) QDs. The addition of small reactant QDs can be repeated to continuously reduce the size distribution. The new method was applied to synthesize PbSe and PbS QDs with extremely narrow size distributions and as a bonus they have hybrid surface passivation. In conclusion, the size distribution of prepared PbSe and PbS QDs are as low as 3.6% and 4.3%, respectively, leading to hexagonal close packing in monolayer and highly ordered three-dimensional superlattice.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantized Electronic Doping towards Atomically Controlled “Charge-Engineered” Semiconductor Nanocrystals
“Charge engineering” of semiconductor nanocrystals (NCs) through so-called electronic impurity doping is a long-standing challenge in colloidal chemistry and holds promise for ground-breaking advancements in many optoelectronic, photonic, and spin-based nanotechnologies. To date, our knowledge is limited to a few paradigmatic studies on a small number of model compounds and doping conditions, with important electronic dopants still unexplored in nanoscale systems. Equally importantly, fine-tuning of charge engineered NCs is hampered by the statistical limitations of traditional approaches. The resulting intrinsic doping inhomogeneity restricts fundamental studies to statistically averaged behaviors and complicates the realization of advanced device concepts based on their advantageous functionalities. We aim to address these issues by realizing the first example of II–VI NCs electronically doped with an exact number of heterovalent gold atoms, a known p-type acceptor impurity in bulk chalcogenides. Single-dopant accuracy across entire NC ensembles is obtained through a novel non-injection synthesis employing ligand-exchanged gold clusters as “quantized” dopant sources to seed the nucleation of CdSe NCs in organic media. Structural, spectroscopic, and magneto-optical investigations trace a comprehensive picture of the physical processes resulting from the exact doping level of the NCs. Gold atoms, doped here for the first time into II–VI NCs, are found to incorporate as nonmagnetic Au + species activating intense size-tunable intragap photoluminescence and artificially offsetting the hole occupancy of valence band states. Fundamentally, the transient conversion of Au + to paramagnetic Au 2+ (5d 9 configuration) under optical excitation results in strong photoinduced magnetism and diluted magnetic semiconductor behavior revealing the contribution of individual paramagnetic impurities to the macroscopic magnetism of the NCs. Altogether, our results demonstrate a new chemical approach toward NCs with physical functionalities tailored to the single impurity level and offer a versatile platform for future investigations and device exploitation of individual and collective impurity processes in quantum confined structures.
36 MATERIALS SCIENCE↗
Cross-Sections of Nanocellulose from Wood Analyzed by Quantized Polydispersity of Elementary Microfibrils
Bio-based nanocellulose has been shown to possess impressive mechanical properties and simplicity for chemical modifications. The chemical properties are largely influenced by the surface area and functionality of the nanoscale materials. However, finding the typical cross-sections of nanocellulose, such as cellulose nanofibers (CNFs), has been a long-standing puzzle, where subtle changes in extraction methods seem to yield different shapes and dimensions. Here, we extracted CNFs from wood with two different oxidation methods and variations in degree of oxidation and high-pressure homogenization. Additionally, the cross-sections of CNFs were characterized by small-angle X-ray scattering and wide-angle X-ray diffraction in dispersed and freeze-dried states, respectively, where the results were analyzed by assuming that the cross-sectional distribution was quantized with an 18-chain elementary microfibril, the building block of the cell wall. We find that the results agree well with a pseudosquare unit having a size of about 2.4 nm regardless of sample, while the aggregate level strongly depends on the extraction conditions. Furthermore, we find that aggregates have a preferred cohesion of phase boundaries parallel to the (110)-plane of the cellulose fibril, leading to a ribbon shape on average.
36 MATERIALS SCIENCE↗
Simultaneous observation of the quantization and the interference pattern of a plasmonic near-field
Surface plasmon polaritons can confine electromagnetic fields in subwavelength spaces and are of interest for photonics, optical data storage devices and biosensing applications. In analogy to photons, they exhibit wave–particle duality, whose different aspects have recently been observed in separate tailored experiments. Here we demonstrate the ability of ultrafast transmission electron microscopy to simultaneously image both the spatial interference and the quantization of such confined plasmonic fields. Our experiments are accomplished by spatiotemporally overlapping electron and light pulses on a single nanowire suspended on a graphene film. The resulting energy exchange between single electrons and the quanta of the photoinduced near-field is imaged synchronously with its spatial interference pattern. In conclusion, this methodology enables the control and visualization of plasmonic fields at the nanoscale, providing a promising tool for understanding the fundamental properties of confined electromagnetic fields and the development of advanced photonic circuits.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Electrical probing of field-driven cascading quantized transitions of skyrmion cluster states in MnSi nanowires
Magnetic skyrmions are topologically stable whirlpool-like spin textures that offer great promise as information carriers for future spintronic devices. To enable such applications, particular attention has been focused on the properties of skyrmions in highly confined geometries such as one-dimensional nanowires. Hitherto, it is still experimentally unclear what happens when the width of the nanowire is comparable to that of a single skyrmion. Here, we achieve this by measuring the magnetoresistance in ultra-narrow MnSi nanowires. We observe quantized jumps in magnetoresistance versus magnetic field curves. By tracking the size dependence of the jump number, we infer that skyrmions are assembled into cluster states with a tunable number of skyrmions, in agreement with the Monte Carlo simulations. Our results enable an electric reading of the number of skyrmions in the cluster states, thus laying a solid foundation to realize skyrmion-based memory devices.
36 MATERIALS SCIENCE↗