Constant External Field Research Articles

A Weyl semimetal from AdS/CFT with flavour

We construct a top-down holographic model of Weyl semimetal states using (3 + 1)-dimensional mathcal{N} = 4 supersymmetric SU(Nc) Yang-Mills theory, at large Nc and strong coupling, coupled to a number Nf ≪ Nc of mathcal{N} = 2 hypermultiplets with mass m. A U(1) subgroup of the R-symmetry acts on the hypermultiplet fermions as an axial symmetry. In the presence of a constant external axial gauge field in a spatial direction, b, we find the defining characteristic of a Weyl semi-metal: a quantum phase transition as m/b increases, from a topological state with non-zero anomalous Hall conductivity to a trivial insulator. The transition is first order. Remarkably, the anomalous Hall conductivity is independent of the hypermultiplet mass, taking the value dictated by the axial anomaly. At non-zero temperature the transition remains first order, and the anomalous Hall conductivity acquires non-trivial dependence on the hypermultiplet mass and temperature.

Один подход к численному решению основного уравнения магнитостатики для конечного цилиндра в произвольном внешнем поле

The magnetostatics direct problem of calculating the resulting magnetic field strength from a homogeneous cylinder of finite dimensions placed in an external magnetic field of arbitrary configuration is considered. With the help of sufficiently voluminous analytical transformations using the basic properties of hypergeometric functions and Legendre functions, the solution of the basic three-dimensional magnetostatic equation for this configuration is reduced to solving of a certain number of systems of three one-dimensional linear integral equations. A simplified form of these systems for special cases of a constant external field and the resulting field on the cylinder axis is obtained.

ENERGY STATES OF PARTICLES IN A QUANTUM SIZED STRUCTURE WITH A COMPLEX SHAPED BAND DIAGRAM

The subject of research in the article is the energy spectrum of a multilayer quantum sized structure with an energy profile of a complex shape. The goal of this work is to study the interaction of quantum-confined and quasi- continuum energy states of particles under the action of an external stationary electric field applied perpendicular to the planes of quantum confinement. The following tasks were solved in the article: The spectrum of eigenfunctions and eigenvalues of particle energy is determined, both in the area of the quantum confinement and in the area of the quasi-continuum. The definition of the eigenfunctions takes into account the fact that the phase of the eigenfunctions changes due to the motion of particles over the quantum well. The following methods were used to solve the set tasks: quantum mechanical modeling of stationary states in a structure with an energy profile of a complex shape; methods of the theory of small perturbations for describing the interaction of particles in such a structure. The following results were obtained: the basic calculation relations of the mathematical model of the energy states of particles and quasiparticles in quantum-limited and quasi-continuum states were obtained within the framework of the quantum-mechanical approach. The interaction of energy states of particles and quasiparticles in each of the bands between quantum-confined and quasi-continuum states is described depending on the external influence. The theory of small perturbations is applied in the paper to assess the degree of interaction. Conclusions: Analysis of the results of modeling the energy spectrum of a structure with two quantum wells, calculated for an unperturbed state and for the case of external action in the form of a stationary electric field, leads to the following conclusions: in the absence of an external field acting on the considered quantum well structure, electrons and holes located above the separation barrier are characterized by a non-monotonically increasing spectrum of energy states. In this case, the particles are predominantly localized above the quantum wells; the action of a constant external electric field on the structure under consideration leads to the manifestation of the quantum-limited Stark effect both for solitary and for multilayer periodic quantum well structures. In this case, the delocalization of the wave functions and the shift of the corresponding energy levels (the lowest energy levels in the structure under consideration) is expressed as strongly as in multilayer symmetric structures. At the same time, the effect is almost invisible for the higher levels. This is especially pronounced for the energy levels lying above the separation barrier. Thus, it can be expected that an equidistant energy spectrum can be realized at a certain external field strength, which in turn should simplify significantly the attainment of the second harmonic generation mode if the structure under consideration is used in the active region of a semiconductor laser.

The Global Stability of M33 in MOND

Abstract The dynamical stability of disk galaxies is sensitive to whether their anomalous rotation curves are caused by dark matter halos or Milgromian dynamics (MOND). We investigate this by setting up a MOND model of M33. We first simulate it in isolation for 6 Gyr, starting from an initial good match to the rotation curve (RC). Too large a bar and bulge form when the gas is too hot, but this is avoided by reducing the gas temperature. A strong bar still forms in 1 Gyr, but rapidly weakens and becomes consistent with the observed weak bar. Previous work showed this to be challenging in Newtonian models with a live dark matter halo, which developed strong bars. The bar pattern speed implies a realistic corotation radius of 3 kpc. However, the RC still rises too steeply, and the central line-of-sight velocity dispersion (LOSVD) is too high. We then add a constant external acceleration field of 8.4 × 10−12 m s−2 at 30° to the disk as a first-order estimate for the gravity exerted by M31. This suppresses buildup of material at the center, causing the RC to rise more slowly and reducing the central LOSVD. Overall, this simulation bears good resemblance to several global properties of M33, and highlights the importance of including even a weak external field on the stability and evolution of disk galaxies. Further simulations with a time-varying external field, modeling the full orbit of M33, will be needed to confirm its resemblance to observations.

Drude weight in systems with open boundary conditions

A many-electron conducting system undergoes free acceleration in response to a macroscopic field. The Drude weight $D$---also called charge stiffness---measures the adiabatic (inverse) inertia of the electrons; the $D$ formal expression requires periodic boundary conditions. When instead a bounded sample is addressed within open boundary conditions, no current flows and a constant (external) field only polarizes the sample: the Faraday cage effect. Nonetheless a low-frequency field induces forced oscillations: we show here that the low-frequency linear response of the bounded system is dominated by the adiabatic inertia and allows an alternative evaluation of $D$. Simulations on model one-dimensional systems demonstrate our main message.

Solutions for a hyperbolic diffusion equation with linear reaction terms

General diffusion processes involve one or more diffusing species and are usually modelled by Fick’s law, which assumes infinite propagation velocity. In this article, searching for the effect of finite propagation speeds in a system with two reacting species, we investigate diffusing and reacting particles governed by a hyperbolic diffusion equation, that is, the Cattaneo equation, which describes a diffusion process with finite propagation velocity, in the presence of a constant external field and reaction terms. These reaction terms are linear and may be related to irreversible and reversible processes, including memory effects, depending on the choices of the reaction rates. We obtain exact solutions for the equilibrium concentrations and explore the rich variety of behaviours exhibited by the species involved in reaction processes. Our results may shine new light into systems with more than one kind of diffusing and reacting particles, as is the case in several industrial and biological process, when finite speeds and memory effects are involved.

MicroEHD Flow Structures under Constant Electric Fields

The results from studying electrohydrodynamic (EHD) vortex flows in a 1-mm gap with different geometry of electrodes and under constant external electric fields are presented. The solution of a transformer oil with iodine was used as a working fluid in which the unipolar conductivity was formed owing to the electro-chemical injection of negative ions from the cathode. The EHD microvortex flow was observed using an optical microscope and snapshot with a digital video camera. The flow lines were fixed with the tracks of light-scattering microparticles 1 micron in size. The rates of flows were up to 10 cm/s at a voltage of 3 kV across the electrodes.

Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes

In the first-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the “N -photon kernel,” where off-shell this kernel appears also in “subleading” terms involving only N − 1 of the N photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the N = 2 case for a recalculation of the one-loop fermion self energy, in D dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation by choosing an unusual momentum-dependent gauge parameter.

Barkhausen pulses caused by domain merging in congruent lithium niobate

The analysis of the shapes of Barkhausen pulses (BPs) was used for the detailed characterization of the domain merging process in congruent lithium niobate LiNbO3 (CLN) crystals. The BPs in ferroelectrics manifest themselves as the sharp peaks in a switching current during polarization reversal by the application of a constant or slow-varying external electric field. Three mechanisms of the BPs were previously proposed: domain nucleation, interaction of the domain walls with the pinning centers, and domain merging. We have revealed the domination of the domain merging mechanism for the generation of the BPs in CLN and classified the scenarios of domain structure evolution after merging in terms of the appearance and transformation of short-lived fast and superfast domain walls. We have shown that the input of merging events reaches 80% of the whole switching process. Two revealed types of BPs corresponding to the merging events considerably differ by duration and shape, thus opening the way for solution of the inverse problem—extracting the quantitative information about the domain kinetics by the analysis of the BPs. This analysis allows extracting the velocities of the fast and superfast walls and provides the possibility to go beyond the temporal resolution of the in situ imaging system in studying the superfast domain wall motion. The proposed analysis is applicable for the faceted growth of polygonal domains in any ferroelectric. It is necessary to point out that the analysis of the BPs allowed characterizing the main part of the domain evolution process in CLN as the fast domain transformations after merging prevail during the polarization reversal.

Trapping Using Molecular Dynamics of Natural Gas in Carbon Nanotubes Under the External Uniform Electric Field

We perform behavioral analysis of natural gas and SYNGAS molecules interacting with a carbon nanotube at an initial simulation temperature of 300 K, and under a uniform electric field, as a gas sensor system using molecular dynamics. Each gas molecule was relaxed for 50 ps outside the carbon nanotube, describing each possible arrangement. A constant external electric field was applied longitudinally to this system, along the length of the carbon nanotube, promoting an evanescent effect, capable of trapping each gas molecule by spinning around it. The electric field intensities were from a range of 10–8 a.u. to 10–1 a.u. were performed, and mean orbit radii and thermodynamic properties were estimated. The results indicate that an external uniform electric field and van der Waals interactions in a carbon-derived nanotube are sufficient to create an evanescent field of attractive potential, presenting it as a practical system for detecting through temperature and ray analysis, of the GN molecules and the SYNGAS.

Propagation of microwave photons along a synthetic dimension

The evenly spaced modes of an electromagnetic resonator are coupled to each other by appropriate time modulation, leading to dynamics analogous to those of particles hopping between different sites of a lattice. This substitution of a real spatial dimension of a lattice with a ``synthetic'' dimension in frequency space greatly reduces the hardware complexity of an analog quantum simulator. Complex control and readout of a highly multimoded structure can thus be accomplished with very few physical control lines. We demonstrate this concept with microwave photons in a superconducting transmission line resonator by modulating the system parameters at frequencies near the resonator's free spectral range and observing propagation of photon wave packets in time domain. The linear propagation dynamics are equivalent to a tight-binding model, which we probe by measuring scattering parameters between frequency sites. We extract an approximate tight-binding dispersion relation for the synthetic lattice and initialize photon wave packets with well-defined quasimomenta and group velocities. As an example application of this platform in simulating a physical system, we demonstrate Bloch oscillations associated with a particle in a periodic potential and subject to a constant external field. The simulated field strongly affects the photon dynamics despite photons having zero charge. Our observation of photon dynamics along a synthetic frequency dimension generalizes immediately to topological photonics and single-photon power levels, and expands the range of physical systems addressable by quantum simulation.

Interaction of a Rectangular Unipolar Pulse with a Two-Level Resonant Medium

The interest in unipolar pulses in optics is related to the possibility of their efficient action on quantum objects. In this work, we study the interaction of a short rectangular unipolar pulse with a two-level resonant medium under conditions that the pulse duration is shorter than the relaxation times of the medium. It is paradoxical that the polarization and the population difference of the medium oscillate not at the Rabi frequency, but, rather, at a frequency that is proportional to the sum of the squared frequency of the resonant transition of the medium and the squared Rabi frequency of the pulse. This phenomenon is similar to the Stark effect, which consists of a shift of the transition frequencies of a medium in a constant external electric field. The possibility of generating radiation at frequencies that exceed the resonant transition frequency of the medium upon its excitation by a rectangular unipolar pulse is discussed.

Lane formation in driven pair-ion plasmas

Lane formation dynamics of driven 2D pair-ion plasmas is investigated in underdamped cases. Extensive Brownian dynamics simulation is performed to study the behavior of the system in the presence of both constant and time-varying external electric fields. Lanes are found to form when like particles move along or opposite to the applied field direction. The lane order parameter has been implemented to detect phase transition. For the constant external field case, investigations are performed at different field strengths, to analyze the phase transition from a disordered to a lane state. It is observed that in this case, the electric field strength must exceed a critical value above which lanes are formed distinctly. For the case of the oscillating electric field, the frequency of the external oscillating field is found to control the lane formation phenomenon. We show that if the frequency of the external field exceeds a critical value, the system exhibits a transition back to the disordered state. A simple method for calculating the critical field strength provides quantitative agreement between the calculated and simulated values of the critical field strength for the case of the constant external electric field. The calculated value of the critical frequency agrees qualitatively with our simulation results for the oscillating external electric field case. A comparative study with the overdamped case has been performed, which suggests that the critical field strength corresponding to the phase transition point is higher for the underdamped case as compared to the overdamped one.

Температурные зависимости транспортных характеристик углеродных наночастиц

Technique for calculating the temperature dependences of transport characteristics of different carbon nanoparticles: single-walled nanotubes, graphene, bilayer graphene in a constant external electric field is proposed. Formulas for conductivity and the diffusion coefficient of electrons in carbon nanostructures obtained analytically and analyzed numerically. Conductivity in single-walled and bilayer carbon nanostructures decreases with increasing temperature. The electrical conductivity of carbon nanoparticles depends nonlinearly on the amplitude of the external constant electric field for various temperatures. With increasing temperature, the coefficient of conductivity decreases. The diffusion coefficient of electrons is independent of temperature for both single-layer and bilayer nanoparticles. A nonlinear dependence of the electron diffusion coefficient on the strength of an external constant electric field is shown. Physical justification of the obtained dependences is propose.

Oscillating nuclear electric dipole moment induced by axion dark matter produces atomic and molecular electric dipole moments and nuclear spin rotation

According to the Schiff theorem, a static nuclear electric dipole moment (EDM) does not produce atomic and molecular EDMs. However, interaction with the axion dark matter field generates nuclear EDMs ${\mathbf{d}}_{N}={\mathbf{d}}_{N}^{0}\mathrm{cos}(\ensuremath{\omega}t)$ which oscillate with the frequency $\ensuremath{\omega}={m}_{a}{c}^{2}/\ensuremath{\hbar}$. These oscillating nuclear EDMs generate atomic and molecular EDMs proportional to ${\ensuremath{\omega}}^{2}$. The resulting atomic and molecular EDMs do not, however, lead to nuclear spin rotation in constant external electric fields. On the other hand, an oscillating electric field penetrates atoms and molecules and can interact with nuclear EDMs. Moreover, if the nuclear EDM oscillation frequency is in resonance with the external field, nuclear spin rotation happens, with the rotation angle growing linearly with time.

Schwinger pair production correction in thermal system

In this paper, we give formal results of Schwinger pair production correction in thermal systems with external background field by using the evolution operator method of thermo field dynamics, where especially tree level correction of thermal photons is considered with linear response approaches by an effective mass shift. We consider initial systems in two types of vacuums as zero temperature and thermal vacuum, respectively, with correction of thermal photons is or not included. As an example we give results of these corrections to pair production for a constant external background electric field.

Electrical conductivity of a hot and dense QGP medium in a magnetic field

We compute the electrical conductivity ($ \sigma_{el} $) in the presence of constant and homogeneous external electromagnetic field for the static quark-gluon plasma (QGP) medium, which is among the important transport coefficients of QGP. We present the derivation of the electrical conductivity by solving the relativistic Boltzmann kinetic equation in the relaxation time approximation in the presence of magnetic field ($ B $). We investigate the dependence of electrical conductivity on the temperature and finite chemical potential in magnetic field. We find that electrical conductivity decreases with the increase in the presence of magnetic field. We observe that $ \sigma_{el} $ at a nonzero $ B $ remains within the range of the lattice and model estimate at $ B\neq 0 $. Further, we extend our calculation at finite chemical potential.

The dynamics of a matter-wave soliton under the effect of a two-dimensional constant external force field

Using the time-dependent variational approach and the numerical solution of the Gross–Pitaevskii (GP) equation, the dynamics of a matter-wave soliton are investigated in a two-dimensional constant external force field. Firstly, the time-dependent variational approach is used to study the movements of the center-of-mass position in a simple harmonic trap and a two-dimensional weakly transmissive reflective barrier. Because the mathematical model for describing soliton dynamics in simple harmonic traps is simple, the analytic dynamical results of a soliton wave packet center-of-mass position is given directly. Since the model describing the weakly transmissive reflective barrier is difficult to solve analytically, we give the Newton’s equation of the center-of-mass position of motion, and then use the numerical solution method to study the movement of the center-of-mass in the case of several parameters. To study the motion of the soliton in the harmonic potential trap in the two-dimensional external force field under rotation, we use the split-step finite difference method to solve the two-dimensional GP equation; the motion of the center-of-mass position is discussed under the conditions of several parameter combinations. The results show that the rotation has a very important influence on the movement of the center-of-mass. When there is no rotation effect, the center-of-mass position acts as a simple harmonic motion under the combined action of the external force field and the potential well. When there is a rotation effect, the center-of-mass position is almost static.

On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field**To the memory of H-O Georgii.

The paper concerns the q-state Potts model (i.e. with spin values in ) on a Cayley tree of degree (i.e. with k + 1 edges emanating from each vertex) in an external (possibly random) field. We construct the so-called splitting Gibbs measures (SGM) using generalized boundary conditions on a sequence of expanding balls, subject to a suitable compatibility criterion. Hence, the problem of existence/uniqueness of SGM is reduced to solvability of the corresponding functional equation on the tree. In particular, we introduce the notion of translation-invariant SGMs and prove a novel criterion of translation invariance. Assuming a ferromagnetic nearest-neighbour spin–spin interaction, we obtain various sufficient conditions for uniqueness. For a model with constant external field, we provide in-depth analysis of uniqueness versus non-uniqueness in the subclass of completely homogeneous SGMs by identifying the phase diagrams on the ‘temperature–field’ plane for different values of the parameters q and k. In a few particular cases (e.g. q = 2 or k = 2), the maximal number of completely homogeneous SGMs in this model is shown to be 2q − 1, and we make a conjecture (supported by computer calculations) that this bound is valid for all and .

Effect of an External Electric Field on the Plasma Parameters of the Lower Ionosphere

The effect of a pulsed (with a duration on the order of 1 ms) and of a constant external electric field on plasma-chemical processes in the lower ionosphere at altitudes of 70–100 km above the Earth’s surface is considered. Interest in these externally stimulated physical settings is associated with traditional radiophysical research and problems of radio-chemical atmospheric physics, which has been actively in recent years due to its various scientific and technical applications. A new page in this field of science (unlike the use of spurious radio signals) opens up the possibility of the purposeful field impact on a GPS receiver on the improvement of work and the further development of satellite navigation systems, which, undoubtedly, has not been discussed previously in the literature. In this work, on the basis of the numerical simulation, the concentrations of the main charged particles and the electron temperature in the presence of a strong external electric field have been calculated at an altitude of 100 km.