Uniform Static Electric Field Research Articles

A revisit on the hydrogen atom induced by a uniform static electric field

In this paper, we revisit the Stark effect of the hydrogen atom induced by a uniform static electric field. In particular, a general formula for the integral of associated Laguerre polynomials was derived by applying the method for Hermite polynomials of degree n proposed in the work (Anh-Tai T.D. et al., 2021 AIP Advances 11 085310). The quadratic Stark effect is obtained by applying this formula and the time-independent non-degenerate perturbation theory to hydrogen. Using the Siegert state method, numerical calculations are performed and serve as data for benchmarking. The comparisons are then illustrated for the ground and some highly excited states to provide an insightful look at the applicable limit and precision of the quadratic Stark effect formula for other atoms with comparable properties.

Diffusivity of individual adsorbed water molecules at an Fe2O3 − Hematite/Water interface under external electric-field conditions

The dynamical properties of physically and chemically adsorbed water molecules at a pristine hematite-(001) surfaces have been studied by non-equilibrium ab-initio molecular dynamics in the constant-volume, constant-temperature ensemble at room temperature, under externally-applied, uniform static electric fields of increasing intensity. Significant alterations in the dipole moment and self-diffusion constant were found vis-à-vis zero-field conditions, as well as shifting of the probability distribution of individual molecular self-diffusivities. For instance, application of static fields was found to increase the self-diffusion of water molecules at the α-hematite Fe2O3 surface, effectively due to some extent of ‘dipole-locking’ in the direction of the applied field.

Integral representations for products of Airy functions and their application for analysis of the Green’s function for a particle in a uniform static field

Abstract Representations for products of two Airy functions with different complex arguments in the form of one-dimensional contour integrals are obtained. These representations are used for analysis of the Green’s function for a charged particle in a uniform static electric field. The integral relation between the stationary and time-dependent Green’s functions is discussed in the sense of its analytical properties for complex energy and field strength. It is shown that the Green’s function can be divided into analytic and non-analytic parts with respect to the field strength near its zero.

Static-to-dynamic field conversion with time-varying media

We theoretically demonstrate that a uniform static electric field distribution can be partially converted to radiation fields when a portion of the medium undergoes a temporal change of its permittivity. An in-depth theoretical investigation of this phenomenon is developed for a dielectric block with a steplike temporal change located inside a waveguide charged with a DC voltage source. Closed analytical expressions are derived for the radiated electric and magnetic fields. The exchange of energy between the electrostatic and electromagnetic fields is discussed. The reconciliation between the seemingly contradictory temporal and spatial boundary conditions for the electric and magnetic fields at the interface of the time-varying dielectric block is analyzed and elucidated. Our findings may provide an alternative solution for generating electromagnetic radiation based on time-varying media.

Molecular Interactions Induced by a Static Electric Field in Quantum Mechanics and Quantum Electrodynamics.

By means of quantum mechanics and quantum electrodynamics applied to coupled harmonic Drude oscillators, we study the interaction between two neutral atoms or molecules subject to a uniform static electric field. Our focus is to understand the interplay between leading contributions to field-induced electrostatics/polarization and dispersion interactions, as considered within the employed Drude model for both non-retarded and retarded regimes. For the first case, we present an exact solution for two coupled oscillators obtained by diagonalizing the corresponding quantum-mechanical Hamiltonian and demonstrate that the external field can control the strength of different intermolecular interactions and relative orientations of the molecules. In the retarded regime described by quantum electrodynamics, our analysis shows that field-induced electrostatic and polarization energies remain unchanged (in isotropic and homogeneous vacuum) compared to the non-retarded case. For interacting species modeled by quantum Drude oscillators, the developed framework based on quantum mechanics and quantum electrodynamics yields the leading contributions to molecular interactions under the combined action of external and vacuum fields.

Water Breakup at Fe2O3-Hematite/Water Interfaces: Influence of External Electric Fields from Nonequilibrium Ab Initio Molecular Dynamics.

The dynamical properties of physically and chemically adsorbed water molecules at pristine hematite-(001) surfaces have been studied by means of nonequilibrium ab initio molecular dynamics (NE-AIMD) in the NVT ensemble at room temperature, in the presence of externally applied, uniform static electric fields of increasing intensity. The dissociation of water molecules to form chemically adsorbed species was scrutinized, in addition to charge redistribution and Grotthus proton hopping between water molecules. Dynamical properties of the adsorbed water molecules and OH– and H3O+ ions were gauged, such as the hydrogen bonds between protons in water molecules and the bridging oxygen atoms at the hematite surface, as well as the interactions between oxygen atoms in adsorbed water molecules and iron atoms at the hematite surface. The development of Helmholtz charge layers via water breakup at Fe2O3–hematite/water interfaces is also an interesting feature, with the development of protonic conduction on the surface and more bulk-like water.

Betaboltz: A Monte-Carlo simulation tool for gas scattering processes

We present an open-source code for the simulation of electron and ion transport for user-defined gas mixtures with static uniform electric and magnetic fields. The program provides microscopic interaction simulation and is interfaced with cross-section tables published by LXCat[1]. The framework was validated against drift velocity tables available in literature obtaining an acceptable match for atomic and non-polar molecular gases with spherical symmetry. The code is written in C++17 and is available as a shared library for easy integration into other simulation applications. Program summaryProgram Title: BetaboltzCPC Library link to program files:https://doi.org/10.17632/hjhx8bj45c.1Licensing provisions: LGPL v3Programming language: C++17Nature of problem: Simulations of electron and ion transport in arbitrary gas mixture under static uniform electric and magnetic fields.Solution method: Particle motion using classical and relativistic equation via interaction sampling using Monte-Carlo techniques.Additional comments including restrictions and unusual features: At the time of writing only static uniform electromagnetic fields are supported. However, the implementation of arbitrary fields can be added given an analytical solution is available. A custom XML format for cross-section was developed, because full compatibility with LXCat [1] XML format was not possible. Cross-section databases in the new format are available in the download section of the LXCat site [2].

Weak-Field Asymptotic Theory of Tunneling Ionization of Atoms and Molecules in an Uniform Static Electric Field

Weak-Field Asymptotic Theory of Tunneling Ionization of Atoms and Molecules in an Uniform Static Electric Field

Photorefractive Effect in NLC Cells Caused by Anomalous Electrical Properties of ITO Electrodes

In a pure nematic liquid crystal (NLC) cell, optically induced charge carriers followed by transports in double border interfaces of orientant/LC and indium-tin-oxide (ITO)/orientant (or LC) can cause removal of screening of the static electric field inside the LC film. This is called surface photorefractive effect (SPR), which induces director field reorientation at a low DC electric field beyond the threshold at a reduced Fréedericksz transition and, as a result, a modulation of the LC effective refractive index. The studies conducted on the photoinduced opto-electrical responses in pure nematic LC cells biased with uniform static DC electric fields support the SPR effect (attributed to the photoelectric activation of the double interfaces). The SPR effect was further studied in LC cells with photoresponsive substrates, which act as a source of a bell-shaped electric field distribution in the LC film if no ITO electrode was employed. In an equipped cell with ITO, the photovoltaic electric field induces charge carrier redistribution in the ITO film, hence the SPR effect. This paper is aimed at highlighting all the evidences supporting ITO film as one of the fundamental sources of the SPR effect in pure NLC cells under the condition of applying low optical power and low DC voltage. An optically induced fringe electric field stemming from inhomogeneous photo-charge profiles near the electrode surfaces is expected in the LC film due to the semiconducting behavior of the ITO layer.

Branched crack patterns in layers of Laponite® dried under electric fields: Evidence of power-laws and fractal scalin>.

In the present work we report crack patterns formed in aqueous Laponite® gel in a rectangular box, while exposed to a uniform static electric field. The crack pattern shows a very interesting tree-like geometry extending from the positive to the negative electrode. At the positive electrode a large number of cracks appear at first and merge with each other in stages thus forming tree-like fractal structures. These structures are reminiscent of the Bethe lattice or Cayley tree. The "trees" divide the system into peds of varying size, with numerous smaller ones on the positively charged end, gradually increasing in size, and decreasing in number towards the negative end. If the cumulative distribution of the number of peds exceeding a certain area in size, is plotted against that area, a power-law relation is obtained. This implies a scale-invariant fractal character of the pattern. For a given system size, the exponent of the power-law has a nearly constant value for different applied voltages. We present an experimental study demonstrating this behaviour and discuss how it compares with similar distributions of river-basin areas and viscous fingers in a Hele-Shaw cell.

One- and two-photon phase-sensitive coherent-control scheme applied to photoionization microscopy of the hydrogen atom

Photoionization microscopy (PM) is an electron imaging method designed for the measurement of the outgoing flux of slow electrons produced by photoionization of atoms in the presence of an external uniform static electric field. The high resolution of PM allows the observation of spatial quantum interference structures which are directly related to the squared modulus of the excited electron's wave function. The PM's range of interest lies above the saddle-point energy, where continuum Stark states are degenerate with quasibound ones (resonances). A principal aim of PM is to provide access to the wave functions of the latter, which in hydrogen atoms ionize exclusively via tunneling (in contrast to the continuum states where the electron escapes freely above the potential barrier). In nonhydrogenic atoms, however, quasibound states are coupled with the continuum ones. Among other consequences, this leads to comparable resonant and continuum excitation strengths and the weakening or disappearance of the resonant manifestations from the recorded PM images. Here we examine theoretically the possibility of bypassing these difficulties by applying two-excitation-pathway interference techniques. For this first case-study we employ the hydrogen atom but we, nevertheless, simulate a nonhydrogenic situation by selecting hydrogenic Stark resonances whose excitation strengths are comparable to or even smaller than the continuum ones. Specifically, we consider the interaction of ground-state atoms with an \ensuremath{\omega}/2\ensuremath{\omega} bichromatic laser field inducing one- and two-photon transitions to the final Stark states. It is shown that, under certain conditions and by appropriately adjusting the intensities of the two laser fields and their relative phase, the uncovering of resonant manifestations from PM images may indeed be achieved. Further work concerning theoretical extensions to complex atoms and possible experimental realizations are also discussed.

Chernobyl’s Lesser Known Design Flaw: The Chernobyl Liquidator Medal—An Educational Essay

The honorary Chernobyl Liquidator Medal depicts pathways of alpha, gamma, and beta rays over a drop of blood, signifying the human health impacts of the Chernobyl accident. A relativistic analysis of the trajectories depicted on the Chernobyl Liquidator Medal is conducted assuming static uniform magnetic and electric fields. The parametric trajectories are determined using the energies of alpha (α) and beta (β) particles relevant to the Chernobyl nuclear power plant accident and compared with the trajectories depicted on the liquidator medal. For minimum alpha particle velocity of 0.0512c, the beta particle trajectory depicted on the medal is highly unlikely to have come from a naturally occurring nuclear decay process. The parametric equations are used to determine the necessary beta energies to reproduce the depicted trajectories. This article documents the unfortunate misrepresentation of a famous scientific experiment on an honorary medal and illustrates the importance of better communication between artists and scientists.

Near-saddle-point-energy photoionization microscopy images of Stark states of the magnesium atom

Photoionization microscopy (PM) is a photoelectron imaging method based on the measurement of the electron current probability density in the case of photoionization of an atom in an external uniform static electric field. The resolution of PM is high enough for observing the quantum oscillatory spatial structure of the outgoing electron flux. We examine the Stark states of the magnesium atom and focus on PM features which are specific to the energy range just above the saddle-point energy. Particularly, the existence of $m$-dependent saddle-point thresholds is clearly demonstrated by following the evolution of the recorded angular distributions with energy. Furthermore, the outer inflection point radii of the radial distributions of the images are generally found to increase with energy monotonically but occasionally abruptly, signaling parabolic channel openings (above which these channels are converted to continua). This observation is in accord with recently reported quantum mechanical PM calculations for hydrogenic systems. More importantly, there are a number of nonmonotonic variations (local maxima) of the outer inflection point. The latter are attributed to the local emergence of an intensity halo at the outer part of the images, a feature relevant to the excitation of quasibound Stark states (resonances). The emergence of the halo for a given resonance is found to depend on the static electric field strength. These observations along with the difficulties in observing resonant effects on the recorded images of nonhydrogenic atoms, such as the medium-size magnesium atom, are discussed in detail.

Research progress of terahertz liquid crystal materials and devices

Liquid crystal (LC) is an excellent tunable functional material which can be controlled by the external stimulus such as electric field, magnetic field and temperature. Terahertz (THz) radiation in a frequency range of 0.1−10.0 THz, has enormous advantages such as a low photon energy, sensitivity to crystal lattice vibration, magnetic spins, hydrogen bonds, intermolecular interaction, and water, and high transparency to non-conducting materials. The THz technology, therefore, has great potential in a diverse range of applications from spectroscopy, security screening to biomedical technology and high-speed wireless communication. But the development of high-performance LC based tunable THz functional devices is still in its infancy stage. The dispersion of LC refractive index induces a comparatively low birefringence in the THz regime. The lack of transparent electrodes makes the electric tuning of LCs difficult to achieve. To achieve certain modulations requires a very thick THz layer, leading to several disadvantages such as high operating voltage, slow response and poor pre-alignment. In this paper, we first present the research progress of large birefringence LCs in THz range. A room-temperature nematic LC NJU-LDn-4 with an average birefringence greater than 0.3 in a frequency range from 0.5 to 2.5 THz is shown in detail. This kind of LC can remarkably reduce the required cell gap, thus reducing the operating voltage and response time. Then we summarize varieties of conventional THz devices based on LC. Many electrodes are used for THz range. Graphene which can be used as a perfect transparent electrode material in THz band is proposed. Not only tunable transmissive but also reflective THz waveplates are introduced. The thickness of the LC layer of the reflective one can be reduced to ~10% of that needed for the same phase shift at a given frequency in a transmissive waveplate. The same tunability as that in the transmissive type just needs half the thickness. We also introduce that LC can generate THz vortex beam based on a photopatterned large birefringence LC. In the area of LC based versatile THz metamaterial devices, the adjacent units of a metasurface layer, such as a fishnet or grating, are usually connected to each other which may cause low-quality (<i>Q</i>) factor and polarization sensitivity, which is undesirable. We emphasize a graphene-assisted high-efficiency tunable THz metamaterial absorber. Few-layer porous graphene is integrated onto the surface of a metasurface layer to provide a uniform static electric field to efficiently control the LC, thereby enabling flexible metamaterial designs. The THz far-field and near-field with large modulation and fast response are realized. A magnetically and electrically polarization-tunable terahertz emitter that integrates a ferromagnetic heterostructure and the large-birefringence liquid crystals is also demonstrated to be able to generate broadband THz radiation and control the polarization of THz waves perfectly as well as LC based THz reflectarray. Last but not least, a temperature-supersensitive cholesteric LC used for THz detection is shown. It can not only measure the beam profiles but also detect the power values of THz waves generated from a nonlinear crystal pumped by a table-top laser. Quantitative visualization based on not only the thermochromic but also the thermal diffusion effect, can be used conveniently and effectively at room temperature. In this review, we summarize the latest progress of liquid crystal materials and components in THz and discuss the possible prospects of the combination of liquid crystal technology and THz technology. We envision that LCs will play a unique role in THz sources, THz functional devices and THz detectors.

Tree-like crack patterns in clay dried in a uniform DC electric field

We report desiccation crack formation on a layer of aqueous Laponite® RD gel, exposed to a uniform static electric field varying from 357 to 928 V m−1. The cracks formed exhibit an interesting tree-like pattern. A large number of cracks (∼70) appear initially at the positive end of the sample. Several neighbouring cracks merge with each other, while proceeding towards the negative end leading to a smaller number of cracks. This process is repeated a few times before the hierarchical pattern thus formed reaches the negative end of the sample. The number of cracks is finally reduced to ∼10. The initial number of cracks increases with increasing field strength. The disc-like Laponite® RD clay particles behave as negatively charged in an aqueous medium, because of the diffusion of positive counterions into the solvent, which form a double layer. The external field causes gradual build up of density of positive counterions towards the negative electrode. The bare Laponite® discs which are negatively charged repel each other to create the cracks at the positive end. We develop a simple model to calculate the charge distribution of counterions along the sample. We offer an explanation for the structure of the anisotropic tree-like crack patterns observed on the basis of this model.

Universal rotation of nanowires in static uniform electric fields in viscous dielectric liquids

The wide utilization of nanomanipulation as a promising approach in microorganisms, nanoelectromechanical systems, and assembly of nanostructures remarks the importance of nanostructures' motion in electric fields. Here, we study the rotational dynamics of metallic and non-metallic nanowires (NWs) in a static uniform electric field in viscous dielectric liquids. For metallic NWs, it has been theoretically shown that the electric field-induced rotation is practically independent of the geometrical dimensions and the electrical properties of NWs. Our experimental results for suspended silver (Ag) NWs in microscope oil are perfectly in agreement with this model. However, in the case of TiO2 NWs, as an example of non-metallic NWs, we surprisingly observe the exact same electromechanical torque as metallic Ag NWs under the same experimental conditions. This is mainly explained by NWs' high aspect-ratio which allows one to ignore the non-axial component of the electric field inside the NWs. Therefore, all high-aspect-ratio metallic Ag and non-metallic TiO2 NWs demonstrate an identical rotational speed in the same dielectric liquid and electric field. This result can be used for the controllable alignment or synchronous rotation of an ensemble of different types of NWs for hybrid and advanced devices.

Photoionization microscopy: Hydrogenic theory in semiparabolic coordinates and comparison with experimental results

Photoionization microscopy (PM) is an experimental method allowing for high-resolution measurements of the electron current probability density in the case of photoionization of an atom in an external uniform static electric field. PM is based on high-resolution velocity-map imaging and offers the unique opportunity to observe the quantum oscillatory spatial structure of the outgoing electron flux. We present the basic elements of the quantum-mechanical theoretical framework of PM for hydrogenic systems near threshold. Our development is based on the computationally more convenient semiparabolic coordinate system. Theoretical results are first subjected to a quantitative comparison with hydrogenic images corresponding to quasibound states and a qualitative comparison with nonresonant images of multielectron atoms. Subsequently, particular attention is paid on the structure of the electron's momentum distribution transversely to the static field (i.e., of the angularly integrated differential cross-section as a function of electron energy and radius of impact on the detector). Such 2D maps provide at a glance a complete picture of the peculiarities of the differential cross-section over the entire near-threshold energy range. Hydrogenic transverse momentum distributions are computed for the cases of the ground and excited initial states and single- and two-photon ionization schemes. Their characteristics of general nature are identified by comparing the hydrogenic distributions among themselves, as well as with a presently recorded experimental distribution concerning the magnesium atom. Finally, specificities attributed to different target atoms, initial states, and excitation scenarios are also discussed, along with directions of further work.

Potential distribution around the charged particle in the collisional weakly ionized plasma in an external electric field

A point-like absorbing charged particle in the uniform anisotropic plasma with an external uniform static electric field is under consideration. The ion and electron motion is described in the drift-diffusion approach with a variable mobility. Small perturbations for plasma parameters are considered. The asymptotic expression for electric potential perturbation at large distances is derived and discussed. The analytical approximation for potential distribution around particle is proposed.

Graphene-assisted high-efficiency liquid crystal tunable terahertz metamaterial absorber.

In this paper, few-layer porous graphene is integrated onto the surface of a metasurface layer to provide a uniform static electric field to efficiently control liquid crystal, thereby enabling flexible metamaterial designs. We demonstrate a tunable cross-shaped metamaterial absorber with different arm lengths driven by this combined metasurface and graphene electrode. The resulting absorber supports a resonant frequency tunable from 0.75 to 1 THz with a high-quality factor, and amplitude modulation of ~80% at these frequencies with an applied voltage of 10 V. Furthermore, the near-field intensity and hot spot distribution can be manipulated over a broad range.

Photoionization microscopy of the lithium atom: Wave-function imaging of quasibound and continuum Stark states

Photoionization of an atom in the presence of a uniform static electric field provides the unique opportunity to expand and visualize the atomic wave function at a macroscopic scale. In a number of seminal publications dating back to the 1980s, Fabrikant, Demkov, Kondratovich, and Ostrovsky showed that this goal could be achieved by projecting slow (meV) photoionized electrons onto a position-sensitive detector and underlined the distinction between continuum and resonant contributions. The uncovering of resonant signatures was achieved fairly recently in experiments on the nonhydrogenic lithium atoms [Cohen et al., Phys. Rev. Lett. 110, 183001 (2013)]. The purpose of the present article is the general description of these findings, with emphasis on the various manifestations of resonant character. From this point of view, lithium has been chosen as an illustrative example between the two limiting cases of hydrogen, where resonance effects are more easily identified, and heavy atoms like xenon, where resonant effects were not observed.