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Based on the electron-ion model, parameters of ball and bead lightning are calculated. The model allows us to estimate maximum size of ball lightning, its energy content, electric charge and magnetic field, to determine equilibrium conditions between positively charged ions located inside and outer shell containing rapidly moving electrons. An explanation is given to the fact that shells are observed inside ball lightning that differ from each other in color of glow. The model describes structure of not only ball lightning, but also bead lightning. The long-term stability of bead lightning is associated with the balance of neighboring beads under action of magnetic force of their attraction and electric force of repulsion, which exceed in magnitude the force of wind pressure., Comment: 34 pages

The scalar and vector potentials of the acceleration field and the pressure field are calculated for the first time for a rotating relativistic uniform system, and the dependence of the potentials on the angular velocity is found. These potentials are compared with the potentials for the non-rotating uniform system that have been found previously. The rotation leads to the appearance of vector potentials, which at each point turn out to be directed along the corresponding linear velocity of rotation. The calculation shows that for rotating stellar objects the contribution to the fields vector potentials from the proper random motion of particles is small compared to the contribution from rotation and may not be taken into account. From the expression for the pressure field potential a relativistic formula follows that relates the pressure, mass density, and mean square velocity of the particles. This formula in the limit of low speeds corresponds to the expression for the pressure in molecular kinetic theory. When calculating the potentials, a new method is used that takes into account the potentials of two different bodies, a cylinder and a sphere, for solving the wave equation of rotating system., Comment: 33 pages

High velocity neutron stars, observed as rapidly moving radio-pulsars, are believed to gain high linear velocities -- kicks -- in aspherical supernova explosions. The mechanism of the kick formation is probably connected with anisotropic neutrino flash, and/or anisotropic matter ejection. In this paper, we investigate a neutron star kick origin in a magnetorotational (MR) supernova explosion model. The simulations have been done for a series of core collapse supernova models with initial equatorially asymmetric magnetic fields. We have realized 2D magnetohydrodynamic simulations, considering the protoneutron star kick and explosion properties in three different asymmetric magnetic field configurations. The simulations show, that in the MR supernova model protoneutron star kicks are formed with velocities up to ~500 km/s, due to asymmetric matter ejection in jets. It may explain the observed kick velocities of some neutron stars, formed in the MR supernovae explosions., Comment: 15 pages, 15 figures, 4 tables, published recently in PRD. This is the accepted version of the paper, which is slightly different from the journal one due to minor language corrections from the editorial staff during production process

We introduce the pCI software package for high-precision atomic structure calculations. The standard method of calculation is based on the configuration interaction (CI) method to describe valence correlations, but can be extended to attain better accuracy by including core correlations via many-body perturbation theory (CI+MBPT) or the all-order (CI+all-order) method, as well as QED corrections via QEDMOD. The software package enables calculations of atomic properties, including energy levels, g-factors, hyperfine structure constants, multipole transition matrix elements, polarizabilities, and isotope shifts. It also features modern high-performance computing paradigms, including dynamic memory allocations and large-scale parallelization via the message-passing interface, to optimize and accelerate computations., Comment: 22 pages, 6 tables, 2 figures

It is shown that in curved spacetime none of the known definitions of four-momentum correspond to the definition, in which all the system particles and fields, including fields outside matter, make an explicit contribution to the four-momentum. This drawback can be eliminated under the assumption that the primary representation of four-momentum is the sum of two nonlocal four-vectors of the integral type with covariant indices. The first of these four-vectors is the generalized four-momentum, found with the help of Lagrangian density. The second four-vector is the four-momentum of fields themselves, and its time component is related to the energy given by tensor invariants. The standard approach makes it possible to find the four-momentum in covariant form only for a free point particle. In contrast, the obtained formulas for calculating the four-momentum components are applied to a stationary and moving relativistic uniform system, consisting of many particles. In this case, the main fields of the system under consideration are taken into account, including the electromagnetic and gravitational fields, the acceleration field and the pressure field. The formalism used includes the principle of least action, charged and neutral four-currents, corresponding four-potentials and field tensors, which ensures unification and the possibility of combining fields into a single interaction. The calculation of the integral vector components shows that the so-called integral vector is not equal to four-momentum and is not a four-vector at all, although it is conserved in a closed system. Thus, the four-momentum cannot be found with the help of an integral vector and components of the system stress-energy tensor, in contrast to how it is assumed in the general theory of relativity., Comment: 79 pages

In state-of-the-art optical lattice clocks, beyond-electric-dipole polarizability terms lead to a break-down of magic wavelength trapping. In this Letter, we report a novel approach to evaluate lattice light shifts, specifically addressing recent discrepancies in the atomic multipolarizability term between experimental techniques and theoretical calculations. We combine imaging and multi-ensemble techniques to evaluate lattice light shift atomic coefficients, leveraging comparisons in a dual-ensemble lattice clock to rapidly evaluate differential frequency shifts. Further, we demonstrate application of a running wave field to probe both the multipolarizability and hyperpolarizability coefficients, establishing a new technique for future lattice light shift evaluations., Comment: 17 pages, 6 figures

This paper presents a study of brane formation in six-dimensional space. There is no a priori assumption of the brane(s) existence. However, the analysis of the generalized Einstein equations reveals that there are a set of metrics describing two static branes even in the absence of matter fields. The trapping of massive particles on branes is a consequence of the metric structure, which prevents these particles from moving between branes. It is shown that the communication between charged particles located on different branes provides by photons. Such positron-electron annihilation could be experimentaly study at the LHC collider. The Higgs field is distributed between the branes in such a way that it can serve as a Higgs portal connecting two worlds located on different branes. The values of the 4D physical parameters depend on the extra metric structure near the branes. A particular metric of the extra space was found to provide the observed value of the Higgs vacuum average. We also found a non-trivial effect of decompactification of the extra space when the Hubble parameter is varied., Comment: 19 pages, 6 figures

Polaritonic crystals - periodic structures where the hybrid light-matter waves called polaritons can form Bloch states - promise a deeply subdiffractional nanolight manipulation and enhanced light-matter interaction. In particular, polaritons in van der Waals materials boast extreme field confinement and long lifetimes allowing for the exploitation of wave phenomena at the nanoscale. However, in conventionally patterned nanostructures, polaritons are prone to severe scattering loss at the sharp material edges, making it challenging to create functional polaritonic crystals. Here, we introduce a new concept of a polaritonic Fourier crystal based on a harmonic modulation of the polariton momentum in a pristine polaritonic waveguide with minimal scattering. We employ hexagonal boron nitride (hBN) and near-field imaging to reveal a neat and well-defined band structure of phonon-polaritons in the Fourier crystal, stemming from the dominant excitation of the first-order Bloch mode. Furthermore, we show that the fundamental Bloch mode possesses a polaritonic bandgap even in the relatively lossy naturally abundant hBN. Thus, our work provides a new paradigm for polaritonic crystals essential for enhanced light-matter interaction, dispersion engineering, and nanolight guiding.

A four-dimensional differential Euler-Lagrange equation for continuously distributed materials is derived based on the principle of least action, and instead of Lagrangian, this equation contains the Lagrangian density. This makes it possible to determine the density of generalized four-momentum in covariant form as derivative of the Lagrangian density with respect to four-velocity of typical particles of a system taken with opposite sign, and then calculate the generalized four-momentum itself. It is shown that the generalized four-momentum of all typical particles of a system is an integral four-vector and therefore should be considered as a special type of four-vectors. The presented expression for generalized four-momentum exactly corresponds to the Legendre transformation connecting the Lagrangian and Hamiltonian. The obtained formulas are used to calculate generalized four-momentum of stationary and moving relativistic uniform systems for the Lagrangian with particles and vector fields, including electromagnetic and gravitational fields, acceleration field and pressure field. It turns out that the generalized four-momentum of a moving system depends on the total mass of particles, on the Lorentz factor and on the velocity of the systems center of momentum. Besides, an additional contribution is made by the scalar potentials of the acceleration field and the pressure field at the center of system. The direction of the generalized four-momentum coincides with the direction of four-velocity of the system under consideration, while the generalized four-momentum is part of the relativistic four-momentum of the system., Comment: 41 pages. Gazi University Journal of Science (2023)

We used the monochromatic soft-x-ray beamline P04 at the synchrotron-radiation facility PETRA III to resonantly excite the strongest $2p-3d$ transitions in neon-like Ni XIX ions, $[2p^6]_{J=0} \rightarrow [(2p^5)_{1/2}\,3d_{3/2}]_{J=1}$ and $[2p^6]_{J=0} \rightarrow [(2p^5)_{3/2}\,3d_{5/2}]_{J=1}$, respectively dubbed 3C and 3D, achieving a resolving power of 15\,000 and signal-to-background ratio of 30. We obtain their natural linewidths, with an accuracy of better than 10\%, as well as the oscillator-strength ratio $f(3C)/f(3D)$ = 2.51(11) from analysis of the resonant fluorescence spectra. These results agree with those of previous experiments, earlier predictions, and our own advanced calculations., Comment: 10 pages, 3 figures, 3 tables, published

The origin and evolution of supermassive black holes (SMBHs) in our universe have sparked controversy. In this study, we explore the hypothesis that some of these black holes may have seeded from the direct collapse of dark energy domains with density significantly higher than the surrounding regions. The mechanism of the origin of such domains relies on the inflationary evolution of a scalar field acting in D dimensions, which is associated with the cosmological constant in our four-dimensional spacetime manifold. Inner space quantum fluctuations of the field during inflation are responsible for the spatial variations of the dark energy density in our space. This finding holds particular significance, especially considering recent evidence from pulsar timing array observations, which supports the existence of a stochastic gravitational wave background consisting of SMBH mergers., Comment: 31 pages, 1 figure, to align with the version published in Universe

Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the concentration of measure phenomenon, including second order concentration inequalities. A detail account is also given in the case of the circle, with a short overview of H\"offding's kernels and covariance identities in the class of periodic functions.

We start with a brief survey on H\"offding's kernels, its properties, related spectral decompositions, and discuss marginal distributions of H\"offding measures. In the second part of this note, one-dimensional covariance representations are considered over compactly supported probability distributions in the class of periodic smooth functions. H\"offding's kernels are used in the construction of mixing measures whose marginals are multiples of given probability distributions, leading to optimal kernels in periodic covariance representations., Comment: arXiv admin note: text overlap with arXiv:2403.19089

This article is the third in the series. It is devoted the calculation of the structure constants for the complex simple Lie algebra of type E_6 and Chevalley commutator formulas., Comment: arXiv admin note: text overlap with arXiv:2312.03439

Scattering-type scanning near-field optical microscope (s-SNOM) has become an essential tool to study polaritons - quasiparticles of light coupled to collective charge oscillations - via direct probing of their near field with a spatial resolution far beyond the diffraction limit. However, extraction of the polariton complex propagation constant from the near-field images requires subtle considerations that have not received necessary attention so far. In this study, we discuss important yet overlooked aspects of the near-field analysis. First, we experimentally demonstrate that the sample orientation inside the s-SNOM may significantly affect the near-field interference pattern of mid-infrared polaritons, leading to an error in momentum measurement up to 7.7% even for the modes with effective index of 12.5. Second, we establish a methodology to correctly extract the polariton damping rate from the interference fringes depending on their origin - the s-SNOM nano-tip or the material edge. Overall, our work provides a unified framework for the accurate extraction of the polariton momentum and damping from the near-field interference fringes., Comment: 15 pages, 4 figures

For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the R\'enyi divergence of infinite order. In terms of densities $p_n$ of $Z_n$, this is a strengthened variant of the local limit theorem taking the form $\sup_x (p_n(x) - \varphi(x))/\varphi(x) \rightarrow 0$ as $n \rightarrow \infty$., Comment: Corrected typos and updated section 11

This article is the second in the series and is devoted to the type G_2. The work consists of two parts. In the first part we calculate the structure constants of the complex simple Lie algebra of type G_2. All structure constants are represented as functions of the structure constants corresponding to extraspecial pairs. The results obtained are used to calculate the commutator Chevalley formulas for [x_r(u),x_s(y)], when the sum r+s is a root. Further, in the second part there is a table of structure constants and Chevalley commutator formulas in the special case, when all structure constants corresponding to extraspecial pairs are positive.

This work is the first in a series of papers devoted to constructing tables of structure constants for the complex simple Lie algebras and to finding an explicit form of Chevalley commutator formulas. The work consists of three parts. In the first part, expressions are found for the structure constants of the complex simple Lie algebra of type F_4 in the form of functions of structure constants corresponding to extraspecial pairs of roots. As a consequence, all Chevalley commutator formulas [x_r(u),x_s(y)] are calculated when the sum r+s is a root. Further, in the second part, tables of structure constants and Chevalley commutator formulas are given in the special case when all constants corresponding to extraspecial pairs are equal to one. Finally, in the third part, directed and weighted graphs associated with root systems are constructed. It is shown that the elements of the exponent of the adjacency matrices of directed graphs are the numbers P_{rs}, where P_{rs} is the number of representations of the root r in the form of a sum of the root s and fundamental roots such that any initial segment of the sum is a root. It is also shown that the elements of an exponent of the weight matrix of a weighted graph are the values of sums arising when calculating complex commutators in Chevalley groups.

We discuss a natural extension of Gilles Pisier's approach to the study of measure concentration, isoperimetry and Poincar\'e-type inequalities. This approach allows one to explore counterparts of various results about Gaussian measure in the class of rotationally invariant probability distribution on Euclidean spaces, including multidimensional Cauchy measures.

Topological insulators generally have dielectric bulk and conductive surface states. Consequently, some of these materials have been shown to support polaritonic modes at visible and THz frequencies. At the same time, the optical properties of topological insulators in the mid-infrared (IR) remain poorly investigated. We employ near-field imaging to probe the mid-IR response from the exfoliated flakes of bismuth (Bi) / selenide (Se) / telluride (Te) / antimony (Sb) crystals with varying stoichiometry - Bi2Se3, Bi2Te2Se, and Bi1.5Sb0.5Te1.7Se1.3 - in pristine form as well as covered by thin flakes of hexagonal boron nitride (hBN). Contrary to theoretical expectations, all three materials exhibit a dielectric response with a high refractive index and with a loss below the experimental detection limit. Particularly, the near-field mapping of propagating phonon-polaritons in hBN demonstrates that these van der Waals crystals act as a practically lossless dielectric substrate with an ultra-high refractive index of up to 7.5 in Bi2Te2Se. Such a unique dielectric crystal would be of great advantage for numerous nanophotonic applications in the mid-IR.

Divalent atoms and ions with a singlet $S$ ground state and triplet $P$ excited state form the basis of many high-precision optical atomic clocks. Along with the metastable $^{3}\mathrm{P}_{0}$ clock state, these atomic systems also have a nearby metastable $^{3}\mathrm{P}_{2}$ state. We investigate the properties of the electric quadrupole $^{1}\mathrm{S}_0$$\leftrightarrow$$^{3}\mathrm{P}_{2}$ transition with a focus on enhancing already existing optical atomic clocks. In particular, we investigate the $^{1}\mathrm{S}_0$$\leftrightarrow$$^{3}\mathrm{P}_{2}$ transition in $^{27}\mathrm{Al}^{+}$ and calculate the differential polarizability, hyperfine effects, and other relevant atomic properties. We also discuss potential applications of this transition, notably that it provides two transitions with different sensitivities to systematic effects in the same species. In addition, we describe how the $^{1}\mathrm{S}_0$$\leftrightarrow$$^{3}\mathrm{P}_{2}$ transition can be used to search for physics beyond the Standard Model and motivate investigation of this transition in other existing optical atomic clocks., Comment: 14 pages, 2 figures

We discuss the way of solving the hierarchy problem. We show that starting at the Planck scale, the three energy scales -- inflationary, electroweak and the cosmological ones can be restored. The formation of small parameters is proposed that leads to a successful solution of the problem. The tools involved in the process are $f(R)$ gravity and inhomogeneous extra dimensions. Slow rolling of a space domain from the Planck scale down to the inflationary one gives rise to three consequences: an infinite set of causally disconnected domains (pocket universes) are nucleated; quantum fluctuations in each domain produce a variety of different fields and an extra-dimensional metric distribution; these distributions are stabilized at a sufficiently low energy scale.

We revisit several results on exponential integrability in probability spaces and derive some new ones. In particular, we give a quantitative form of recent results by Cianchi-Musil and Pick in the framework of Moser-Trudinger-type inequalities, and recover Ivanisvili-Russell's inequality for the Gaussian measure. One key ingredient is the use of a dual argument, which is new in this context, that we also implement in the discrete setting of the Poisson measure on integers.

This paper discusses the origin of the small parameters with the aim of explaining the Hierarchy problem. The flexible extra dimensions are an essential tool in the process by which physical parameters are formed. The evolution of a multidimensional metric starts at the Planck scale and is completed with the static extra-dimensional metric and the 4-dim de Sitter space at high energies, where the exponential production of causally disconnected universes begins. Quantum fluctuations independently distort the metric within these universes, causing inflationary processes within them. Some of these universes tend asymptotically towards states characterised by small Hubble parameters. The effective parameter reduction applied to the Higgs sector of the Standard Model is explained by the presence of small-amplitude distributions of a scalar field in a fraction of these universes., Comment: 12 pages, 4 figures

We investigate ultrafast harmonic generation (HG) in Si:B, driven by intense pump pulses with fields reaching ~100 kV/cm and a carrier frequency of 300 GHz, at 4 K and 300 K, both experimentally and theoretically. We report several novel findings concerning the nonlinear charge carrier dynamics in intense sub-THz fields. (i) Harmonics of order up to n=9 are observed at room temperature, while at low temperature we can resolve harmonics reaching even n=13. The susceptibility per charge carrier at moderate field strength is as high as for charge carriers in graphene, considered to be one of the materials with the strongest sub-THz nonlinear response. (ii) For T=300 K, where the charge carriers bound to acceptors are fully thermally ionized into the valence subbands, the susceptibility values decrease with increasing field strength. Simulations incorporating multi-valence-band Monte-Carlo and finite-difference-time-domain (FDTD) propagation show that here, the HG process becomes increasingly dominated by energy-dependent scattering rates over the contribution from band non-parabolicity, due to the onset of optical-phonon emission, which ultimately leads to the saturation at high fields. (iii) At T=4 K, where the majority of charges are bound to acceptors, we observe a drastic rise of the HG yields for internal pump fields of 30 kV/cm, as one reaches the threshold for tunnel ionization. We disentangle the HG contributions in this case into contributions from the initial 'generational'- and subsequent band-nonlinearities, and show that scattering seriously degrades any coherent recollision during the subsequent oscillation of the holes.

A general exact weak solution to the nonlinear equation of the conservation of the absolute vorticity in a thin layer of an incompressible medium on a rotating sphere is proposed. It takes into account the helicity of the point vortices and the non-uniformity of the depth of the layer. This is used to develop a model of the observed interactions of spiral atmospheric vortices. The fusion of two point helical vortices (HVs) on the rotating sphere is considered. We also analyze the prognostic applicability of the dynamics of the HVs for modeling the abrupt changes observed in the trajectories of tropical cyclones and their landfall in comparison with the traditional approach. The analytical condition for chiral symmetry violation related to the direction of the movement of the center of a helical cyclone is obtained., Comment: 45 pages, 7 figures

New analytical solution of the piston and shock evolution for the wire electrical explosion in water is obtained. This is provided on the base of the compressible Euler equations without usually a prior introduction of any self-similarity hypothesis. It is shown that diverging cylindrical shock is transformed into acoustic wave in a finite time, even without taking into account of dissipation. The correspondence with experimental data on underwater electrical explosion of thin wire is represented., Comment: 2 figures

We propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn$^{2+}$ ions confined in a linear RF Paul trap. Sn$^{2+}$ has a unique combination of features that is not available in previously considered ions: a $^1$S$_0$ $\leftrightarrow$ $^3$P$_0$ clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn$^{2+}$ Coulomb-crystal clocks., Comment: 15 pages, 5 figures, 3 tables

We discuss the model of the primordial black holes formation at the reheating stage. These small massive black holes appear due to specific properties of the compact extra dimensions. The latter gives rise the low energy model containing the effective scalar field potential capable for the domain walls production. Formed during inflation, these walls are quite dense so they collapse soon after inflation ends. The discussion is performed within the scope of multidimensional $f(R)$-gravity., Comment: 11 pages, 4 figures