Classical Electron Research Articles

Analytical solution of the Sommerfeld–Page equation

The Sommerfeld–Page equation describes the non-relativistic dynamics of a classical electron modeled by a sphere of finite size with a uniform surface charge density. It is a delay differential equation, and almost no exact solution of this equation was known until recently. However, progress has been made, and an analytical solution was recently found for an almost identical delay differential equation, which arose in the context of the mathematical modeling of the COVID-19 epidemics. Inspired by this research, we offer a pedagogical exposition of how one can find an analytical solution of the Sommerfeld–Page equation.

Tyramine as a Prolific Coformer in Crystal Engineering: Insights from Classical Crystal Structure Analysis and Electron Density Studies

Tyramine as a Prolific Coformer in Crystal Engineering: Insights from Classical Crystal Structure Analysis and Electron Density Studies

Hemifusomes and Interacting Proteolipid Nanodroplets Mediate Multi-Vesicular Body Formation.

The complex, pleiomorphic membrane structure of the vesicular components within the endolysosomal system has been appreciated through decades of classical electron microscopy. However, due to the heavy fixation and staining required in these approaches, in situ visualization of fragile intermediates between early endosomes, late endosomes and ultimately multivesicular bodies (MVBs), remains elusive, raising the likelihood that other structures may have also been overlooked. Here, using in situ cryo-electron tomography in four mammalian cell lines, we discover heterotypic hemifused vesicles that share an extended hemifusion diaphragm, associated with a 42nm proteolipid nanodroplet (PND). We term this previously undescribed vesicular organelle-complex, "hemifusome". Hemifusomes make up approximately 10% of the organelle pool of the endolysosomal system, but do not participate directly in transferrin-mediated endocytosis. Hemifusomes exist in compound conformations and also contain intraluminal vesicles. Based on their range of morphologies, and the consistent presence of the PND at sites of compound hemifused vesicles, we propose that hemifusomes function as platforms for vesicular biogenesis mediated by the PND. These findings offer direct in situ evidence for a long-lived hemifusion diaphragm, and a new, ESCRT-independent model for the formation of late endosomes containing intraluminal vesicles and ultimately MVBs.

Enigmatic factor of 4/3 in electromagnetic momentum of a moving spherical capacitor

The electromagnetic energy–momentum of a moving charged spherical capacitor may be calculated by a 4-vector Lorentz transformation from the energy in the rest frame. However, energy–momentum of the moving system computed directly from electromagnetic fields yields extra terms; in particular a factor of 4/3 in momentum appears, similar to that encountered in the classical electron model, where this enigmatic factor has been a source of confusion for more than a century. There have been many attempts to eliminate this ‘unwanted’ factor, noteworthy among them is a modification in electromagnetic field energy–momentum definition that has entered even standard textbooks. Here it is shown that in a moving charged spherical capacitor, such a factor of 4/3 in the electromagnetic momentum arises naturally from electromagnetic forces in system or equivalently from terms in the Maxwell stress tensor; contributions that do not otherwise show up in 4-vector transformations. A similar factor of 4/3 in the momentum of a perfect fluid comprising a randomly moving ultra-relativistic gas molecules or an isotropic photon gas, filling an uncharged spherical capacitor in motion, appears owing to the contribution of pressure. Thus, genesis of the ‘enigmatic’ factor of 4/3 can be traced to pressure or stress whose presence in the system may even be of non-electromagnetic origin and where the proposed modifications in energy–momentum definition do not even come into picture, implying there is no justification in modifying the standard definition of electromagnetic energy–momentum.

Coherent electron phase-space manipulation by combined elastic and inelastic light-electron scattering

Abstract Photon-Induced Near-field Electron Microscopy (PINEM), Kapitza-Dirac (KD) gratings, and ponderomotive phase plates are examples of techniques in which the wave function of an electron in free space is manipulated using light fields: Free Electron Quantum Optics (FEQO). These effects are usually treated in separate theoretical frameworks. In this paper we present a unified, two-pronged framework that can be used to describe and numerically evaluate the performance of a number of FEQO-based electron-optical elements. The first part is an extension of an existing analytical treatment of PINEM, based on solving a relativistically corrected Schrödinger equation. The extension covers both second-order contributions to PINEM and the Kapitza-Dirac effect. The second, novel element of the approach is based on electron wavefront reconstruction by evaluating the quantum mechanical phase along a bundle of classical electron trajectories. The quasi-classical (but fully relativistic) approach lends itself to simulating a wide variety of FEQO devices, including the examples mentioned. We apply both approaches to a few specific experimental configurations: mirror-based first-order PINEM, second-order PINEM in very high laser intensity, and Kapitza-Dirac diffraction. The results show excellent agreement between the analytical results and the quasi-classical simulations. Finally, we propose a setup that combines KD and PINEM to allow for simultaneous coherent energy and transverse momentum shaping of an electron beam, and present simulation results thereof.

Modulation of H atom photoelectron momentum distribution by chirped laser pulses of different wavelengths

The wavelength dependence of the holographic interference structure in the photoelectron momentum distribution (PMD) of hydrogen atoms under a few-cycle chirped laser field is investigated using a two-dimensional (2D) semiclassical two-step (SCTS) model. Under the constraint of a fixed chirp parameter, we observe an amplification in the impact of the chirp parameter on the laser field waveform as the wavelength increases. This enhancement facilitates effective modulation of the ionization time window. As the wavelength reaches a certain threshold, the double-slit interference pattern undergoes an observable expansion towards the left. Furthermore, based on the variations in X-axis momentum (Px) concerning ionization time at different wavelengths and the corresponding distribution of classical electron trajectories at those wavelengths, we present a more comprehensive explanation for the expansion of interference patterns. This expansion can be attributed to changes in wavelength, which result in modifications to the laser field’s waveform, consequently leading to a significant acceleration of ionized electrons when exposed to chirped laser pulses. It is worth noting that by tuning the negative chirp parameter, the leftward expansion of the double-slit interference pattern can also be achieved, particularly when shorter wavelengths of chirped laser pulses are employed.

An analytical model to ascertain A.C. electrical conductivity of metal matrix composites

ABSTRACT With regard to an inherent understanding of electrical conductivity exhibited by monolithic metals and alloys system and metal matrix composite system under alternating current field, a long-standing unresolved issue, an analytical model is developed following classical free electron theory along with a typical conceptualisation of ‘effective relaxation time’ that combines conventional relaxation time (in view of collision of free electrons with lattice defects) and the time between successive cyclic reversals of electric field (the inverse of frequency). Two prime phenomena (electron scattering and polarisation at particle–matrix interface) are further conceived for metal matrix composite system containing particles. The developed model is found to closely follow (% deviation << 10) the available experimental result in the literature on A.C. electrical conductivity of 6063Al alloy and 6063Al–TiO2 composite systems. The model further ascertains certain system-specific parameters; such as, relaxation time under A.C. field, effective scattering factor and effective relaxation time aid from interface polarisation to specify the system behaviour under alternating current field. Accordingly, the model adequately explains the declining trend of A.C. electrical conductivity with increasing frequency in monolithic alloy system and an enhancement of A.C. electrical conductivity in metal matrix composite system in the presence of particles together with a non-declining trend even on increasing frequency.

1D drift-kinetic numerical model based on semi-implicit particle-in-cell method

The paper presents a new one-dimensional drift-kinetic electrostatic model based on the particle-in-cell method and capable of simulating the processes of plasma heating and confinement in mirror traps. The most of particle and energy losses in these traps occur along the magnetic field lines. The key role in limiting these losses is played by the ambipolar electric potential which creates a potential barrier for electrons and significantly reduces the heat flux that, without this barrier, would go to wall due to the classical electron thermal conductivity. However, modeling the formation of such a potential on real spatial and temporal scales of experiments is a challenging problem, since it requires a detailed description of not only ion, but also electron kinetics. In this work, we propose to solve the problem of taking into account electron kinetic effects on the time scale of plasma confinement in a mirror trap using the particle-in-cell method adapted to the approximate drift-kinetic equations of plasma motion. Unlike other electrostatic particle-in-cell models, which use fully implicit schemes to solve the nonlinear system of Vlasov-Poisson and Vlasov-Ampere equations, we propose a semi-implicit approach. By analogy with the Energy Conserving Semi-Implicit Method (ECSIM), it allows for precise conservation of energy and reduces the procedure for finding the electric field to inverting a tridiagonal matrix without multiple nonlinear iterations. Such a model will be useful for simulating not only collisional losses of hot plasma in fusion experiments, but also for studying the features of creating cold starting plasma in mirror traps using plasma or electron guns.

Glory interference spectroscopy in Sr atom

Slow (meV) photoelectron imaging spectroscopy is employed in the experimental study of near-threshold photoionization of strontium atoms in the presence of an external static electric field. Specifically, the study is devoted to the glory effect, that is, the appearance of an intense peak at the center of the recorded photoelectron images, when dealing with m= 0 final ionized Stark states (m denoting the magnetic quantum number). This critical effect is formally identical to that encountered in classical scattering theory, where, for a nonzero value of the impact parameter, the zero-crossing of the deflection function leads to a divergent classical differential cross section. By recording the magnitude variation of this glory peak as a function of electron excitation energy, we observe that, besides the traces of classical origin, it also exhibits intense quantum interference and beating phenomena, above and below the zero-static-field ionization threshold. We study both, single- and two-photon ionization of Sr, thus enabling a comparison not only between the different excitation schemes, but also with an earlier work devoted to two-photon ionization of Mg atom by Kalaitzis et al (2020 Phys. Rev. A 102 033101). Our recordings are analyzed within the framework of the Harmin–Fano frame transformation Stark effect theory that is applied to both the hydrogen atom and a non-hydrogenic one simulating Sr. We discuss the various aspects of the recorded and calculated glory interference and beating structures and their ‘short time Fourier transforms’ and classify them as either atom-specific or atom independent. In particular, we verify the ‘universal’ connection between the glory oscillations above the zero-field threshold and the differences between the origin-to-detector times of flight corresponding to pairs of classical electron trajectories that end up to the image center.

Chemical bond reorganization in intramolecular proton transfer revealed by ultrafast X-ray photoelectron spectroscopy

Time-resolved X-ray photoelectron spectroscopy (TR-XPS) is used in a simulation study to monitor the excited state intramolecular proton transfer between oxygen and nitrogen atoms in 2-(iminomethyl)phenol. Real-time monitoring of the chemical bond breaking and forming processes is obtained through the time evolution of excited-state chemical shifts. By employing individual atomic probes of the proton donor and acceptor atoms, we predict distinct signals with opposite chemical shifts of the donor and acceptor groups during proton transfer. Details of the ultrafast bond breaking and forming dynamics are revealed by extending the classical electron spectroscopy chemical analysis to real time. Through a comparison with simulated time-resolved photoelectron spectroscopy at the valence level, the distinct advantage of TR-XPS is demonstrated thanks to its atom specificity.

Lactate oxidation in Paracoccus denitrificans

Paracoccus denitrificans has a classical cytochrome-dependent electron transport chain and two alternative oxidases. The classical transport chain is very similar to that in eukaryotic mitochondria. Thus, P. denitrificans can serve as a model of the mammalian mitochondrion that may be more tractable in elucidating mechanisms of regulation of energy production than are mitochondria. In a previous publication we reported detailed studies on respiration in P. denitrificans grown aerobically on glucose or malate. We noted that P. denitrificans has large stores of lactate under various growth conditions. This is surprising because P. denitrificans lacks an NAD+-dependent lactate dehydrogenase. The aim of this study was to investigate the mechanisms of lactate oxidation in P. denitrificans. We found that the bacterium grows well on either d-lactate or l-lactate. Growth on lactate supported a rate of maximum respiration that was equal to that of cells grown on glucose or malate. We report proteomic, metabolomic, and biochemical studies that establish that the metabolism of lactate by P. denitrificans is mediated by two non-NAD+-dependent lactate dehydrogenases. One prefers d-lactate over l-lactate (D-iLDH) and the other prefers l-lactate (L-iLDH). We cloned and produced the D-iLDH and characterized it. The Km for d-lactate was 34 μM, and for l-lactate it was 3.7 mM. Pyruvate was not a substrate, rendering the reaction unidirectional with lactate being converted to pyruvate for entry into the TCA cycle. The intracellular lactate was ∼14 mM such that both isomers could be metabolized by the enzyme. The enzyme has 1 FAD per molecule and utilizes a quinone rather than NAD + as an electron acceptor. D-iLDH provides a direct entry of lactate reducing equivalents into the cytochrome chain, potentially explaining the high respiratory capacity of P. denitrificans in the presence of lactate.

Advances in exploration of photoinduced electron transfer reactions involving small molecules probed by magnetic field effect

The review focuses on photoinduced electron transfer (PET) reactions between small molecules and various kinds of chemical and biological systems using a weak external magnetic field (MF). Laser flash photolysis is a competent tool to characterize the intermediates which are formed due to PET. A weak MF, very close to the hyperfine interaction of the system, has the potential to inhibit or enhance reaction channels for singlet and triplet states, which eventually effects the product distribution. At first, well-documented examples of PET involving small molecules like derivatives of phenazines, carbazoles and acridines with classical electron donors in varying homogeneous and heterogeneous media have been discussed and the influence of a weak MF on the dynamics of PET is highlighted. Secondly, utilization of magnetic field effect (MFE) to probe PET in protein pockets has been described. Thirdly, an extensive discussion on PET involving nucleobases, nucleosides, nucleotides and nucleic acids and subsequent MFE on such reactions has been reported. Next, MFE has been exploited to study PET involving nanomaterials. Finally, some very recent studies of MFE have been discussed. Thus, this review is an attempt to unravel various aspects of PET in a large number of systems of varying dimensions by means of several facets of MFE like B1/2 parameter, its capability to authenticate the initial spin state and distance dependence property.

Structure of root nodules in &lt;i&gt;Laburnum anagyroides&lt;/i&gt; Medik.

The structure of the &lt;i&gt;Laburnum anagyroides&lt;/i&gt; root nodules was studied by means of classical light and transmission electron microscopy methods. The ability of cross-inoculation and effective nodulation by rhizobial microsymbionts, effective in other genistean species, was not confirmed in &lt;i&gt;L. anagyroides&lt;/i&gt;. However, the seedlings were successfully albeit ineffectively nodulated by non-identified rhizobia from soil sampled under established &lt;i&gt;L. anagyroides&lt;/i&gt; trees. The microscopic (ultra)structure of these nodules met the basic criteria of genistoid nodules: their meristem was apically positioned and contained two domains (infected and non-infected one), non-bacteroidal rhizobia persisted in apoplast enclaves, and intra-nodule rhizobial infection was passed from cell to cell by host cell division and not by infection threads. The developmental disturbances detected in the nodules (primarily, formation of multi-bacteroid sacs instead of typical single-bacteroid symbiosomes and proliferation apoplast enclaves with accompanying cell wall discontinuities) suggested that the host plant incorrectly recognized the microsymbiont used in the present study.

The Search for the Origin of the Quantum Conditions under the Paradigm of Absolute Space

This study deals with the physical (not the mathematical) origin of the quantum conditions. The assumption of an absolute space together with the speed of 369.5 km/s of the sun leads to cycloidal or helical orbits of the electron around the proton. This kind of orbits is a previously unnoticed fact and not compatible with the model of a closed circular standing wave. It is the aim of this study to search for alternative models. The Alternating Field model (AFM) assumes the existence of alternating fields for both the proton and the electron. The Higgs-field provides the energy requirements. By Puthoff’s effect, adapted for the electrostatic field, the electron changes its Compton frequency according to its position in the field. The interference of the alternating fields of the proton and the electron causes beats that are integer multiples of the orbital frequencies when the electron moves on Bohr’s orbits. Important results of this study are: The electrostatic Schwarzschild-radius is exactly half the value of the classical electron radius. Bohr’s first three principal quantum numbers, 1, 2, 3, are reproduced as 1.000052, 2.000214, and 3.000685. A two-dimensional simulation shows that the AFM causes orbits with ribbon shape. A formula, using only the orbital frequencies of the two innermost circular orbits, can predict the shortest wavelength of the Lyman series. The AFM is still incomplete. E.g., it does not prevent illegal orbits, but only indicates them. Also, the AFM does not use the magnetic core field of the proton. On the other hand, the model has produced results showing that Newton’s absolute space and the QM are compatible.

Semiclassical reaction rate constant of non-adiabatic system by means of initial value representation

We applied the semiclassical initial value representation (SC-IVR) method with the classical electron analog to deal with electronically non-adiabatic reactive barriers and calculated the thermal reaction rate constant. The symmetric form of the flux–flux correlation function is used, and the matrix element of the Boltzmannized flux operator is derived using imaginary-time path integral techniques. This combined use of non-adiabatic SC-IVR and non-adiabatic path-integral sampling (NA-IVR&amp;PI) is beyond the treatment of mean-field, and we analyze its performance in comparison with some existing mean-field methods for different scenarios of potential energy surface. We found a systematically better performance. One exception is the deep tunneling regime, where the mean-field ring-polymer instanton is superior. In the golden rule limit, where all these mean-field methods break down, the significant advantage of NA-IVR&amp;PI is shown by using the electronic states for description of the dividing surface.

IR-finite thermal acceleration radiation

A charge accelerating in a straight line following the Schwarzschild–Planck moving mirror motion emits thermal radiation for a finite period. Such a mirror motion demonstrates quantum purity and serves as a direct analogy of a black hole with unitary evolution and complete evaporation. Extending the analog to classical electron motion, we derive the emission spectrum, power radiated, and finite total energy and particle count, with particular attention to the thermal radiation limit. This potentially opens the possibility of a laboratory analog of black hole evaporation.

Epimorphic development in tropical shallow-water Nymphonidae (Arthropoda: Pycnogonida) revealed by fluorescence imaging

BackgroundExtant lineages of sea spiders (Pycnogonida) exhibit different types of development. Most commonly, pycnogonids hatch as a minute, feeding protonymphon larva with subsequent anamorphic development. However, especially in cold water habitats at higher latitudes and in the deep sea, some taxa have large, lecithotrophic larvae, or even undergo extended embryonic development with significantly advanced postlarval hatching stages. Similar biogeographic trends are observed in other marine invertebrates, often referred to as “Thorson’s rule”.ResultsTo expand our knowledge on the developmental diversity in the most speciose pycnogonid genus Nymphon, we studied the developmental stages of the two tropical representatives N. floridanum and N. micronesicum., We compared classical scanning electron microscopy with fluorescence-based approaches to determine which imaging strategy is better suited for the ethanol-fixed material available. Both species show epimorphic development and hatch as an advanced, lecithotrophic postlarval instar possessing the anlagen of all body segments. Leg pairs 1–3 show a considerable degree of differentiation at hatching, but their proximal regions remain coiled and hidden under the cuticle of the hatching instar. The adult palp and oviger are not anteceded by three-articled larval limbs, but differentiate directly from non-articulated limb buds during postembryonic development.ConclusionsFluorescence imaging yielded more reliable morphological data than classical scanning electron microscopy, being the method of choice for maximal information gain from rare and fragile sea spider samples fixed in high-percentage ethanol. The discovery of epimorphic development with lecithotrophic postlarval instars in two small Nymphon species from tropical shallow-water habitats challenges the notion that this developmental pathway represents an exclusive cold-water adaptation in Nymphonidae. Instead, close phylogenetic affinities to the likewise more direct-developing Callipallenidae hint at a common evolutionary origin of this trait in the clade Nymphonoidea (Callipallenidae + Nymphonidae). The lack of functional palpal and ovigeral larval limbs in callipallenids and postlarval hatchers among nymphonids may be a derived character of Nymphonoidea. To further test this hypothesis, a stable and well-resolved phylogenetic backbone for Nymphonoidea is key.

Weak measurements and quantum-to-classical transitions in free electron–photon interactions

How does the quantum-to-classical transition of measurement occur? This question is vital for both foundations and applications of quantum mechanics. Here, we develop a new measurement-based framework for characterizing the classical and quantum free electron–photon interactions and then experimentally test it. We first analyze the transition from projective to weak measurement in generic light–matter interactions and show that any classical electron-laser-beam interaction can be represented as an outcome of weak measurement. In particular, the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement. A universal factor, exp left(-{Gamma }^{2}/2right), quantifies the measurement regimes and their transition from quantum to classical, where Gamma corresponds to the ratio between the electron wavepacket size and the optical wavelength. This measurement-based formulation is experimentally verified in both limits of photon-induced near-field electron microscopy and the classical acceleration regime using a DLA. Our results shed new light on the transition from quantum to classical electrodynamics, enabling us to employ the essence of the wave-particle duality of both light and electrons in quantum measurement for exploring and applying many quantum and classical light–matter interactions.

High-order harmonic interferometry for the study of intensity-dependent dipole phase

Abstract High-order harmonics are ideal probes to resolve the attosecond dynamics of strong field recollision process. In this work, an easy-to-implement phase mask is utilized to covert the Gaussian beam to TEM01 transverse electromagnetic mode, allowing the realization of two source interferometry of high-order harmonics. We experimentally measured the intensity-dependence of dipole phase directly with high-order harmonic interferometry, in which the driving laser intensity can be precisely adjusted. The classical electron excursion simulations reproduce the experimental findings quite well, demonstrating that Coulomb potential plays subtle roles on the movement of electrons for harmonics near the ionization threshold. This work is of great importance for precision measurements of ultrafast dynamics in strong-field physics.

A quantum physics layer of epigenetics: a hypothesis deduced from charge transfer and chirality-induced spin selectivity of DNA

BackgroundEpigenetic mechanisms are informational cellular processes instructing normal and diseased phenotypes. They are associated with DNA but without altering the DNA sequence. Whereas chemical processes like DNA methylation or histone modifications are well-accepted epigenetic mechanisms, we herein propose the existence of an additional quantum physics layer of epigenetics.ResultsWe base our hypothesis on theoretical and experimental studies showing quantum phenomena to be active in double-stranded DNA, even under ambient conditions. These phenomena include coherent charge transfer along overlapping pi-orbitals of DNA bases and chirality-induced spin selectivity. Charge transfer via quantum tunneling mediated by overlapping orbitals results in charge delocalization along several neighboring bases, which can even be extended by classical (non-quantum) electron hopping. Such charge transfer is interrupted by flipping base(s) out of the double-strand e.g., by DNA modifying enzymes. Charge delocalization can directly alter DNA recognition by proteins or indirectly by DNA structural changes e.g., kinking. Regarding sequence dependency, charge localization, shown to favor guanines, could influence or even direct epigenetic changes, e.g., modification of cytosines in CpG dinucleotides. Chirality-induced spin selectivity filters electrons for their spin along DNA and, thus, is not only an indicator for quantum coherence but can potentially affect DNA binding properties.ConclusionsQuantum effects in DNA are prone to triggering and manipulation by external means. By the hypothesis put forward here, we would like to foster research on “Quantum Epigenetics” at the interface of medicine, biology, biochemistry, and physics to investigate the potential epigenetic impact of quantum physical principles on (human) life.