Vol 164, No 1 (2023)

A new method is proposed for determining level splitting Δ in a double-well 1D potential. Two “partner” functions (one symmetric Ψ₊ and the other antisymmetric Ψ_–) are determined. From these functions, potentials V₊(x) and V_–(x) and energies E+0">$E_{+}^0$ and E−1">$E_{-}^1$ corresponding to them are determined from the Schrödinger equation. A unique property of Ψ₊ and Ψ_– is identity E+0">$E_{+}^0$ = E−1">$E_{-}^1$, which makes it possible to determine Δ from the perturbation theory in parameter V₊(x) – V_–(x). For a double-well oscillator potential, the expression for the level splitting, which connects the instanton and single-well limits, is obtained. These results can be employed in the field theory, for which the possibility of obtaining instanton solutions from perturbation theory has been discussed more than once. A number of potentials are considered, for which the value of Δ can be determined without using the semiclassical approximation. Singular potentials of the funnel type are analyzed. The value of Δ determined in this study is compared with the results of numerical solution of the Schrödinger equation for the instanton potential.

The effect of a dielectric film on the surface of conducting dust particles on their electrostatic interaction is investigated. Special attention is paid to the case when the radius of one of particles is much larger than the radius of the other particle and to a nonuniform distribution of the surface charge with variants of equilibrium free charge distribution on each of the macroparticles over the entire surface and over the left and/or right hemispheres. The technique for calculating of slowly converging series is worked out using the hypergeometric Gauss functions and by introducing new functions for which recurrent relations and numerical calculation technique were determined.

The correspondence of the results obtained in the Neutrino-4 experiment with the results of the NEOS, DANSS, STEREO, and PROSPECT experiments at reactors, the MiniBooNE, LSND, and MicroBoone experiments at accelerators, and the IceCube and BEST experiments with a ⁵¹Cr neutrino source is analyzed. The agreement between the results of the Neutrino-4 experiment, the BEST experiment, and the gallium anomaly on the mixing angle is discussed. The discrepancy between the results of the listed direct experiments with the results of the reactor anomaly, as well as with constraints from solar and cosmological data, is discussed. It is shown that the results of these direct experiments on the search for sterile neutrinos and the IceCube experiment do not contradict the Neutrino-4 experiment within the 3 + 1 neutrino model within 3σ contours of experimental errors. The sterile neutrino parameters from the Neutrino-4 and BEST experiments make it possible to estimate the sterile neutrino mass as m₄ = (2.70 ± 0.22) eV and the effective mass of the electron neutrino as m4νe">$m_{4{\nu }_e}$ = (0.86 ± 0.21) eV. The matrix of the absolute values of the 3 + 1 neutrino model mixing parameters and the mixing scheme are presented.

Motivated by recent experimental data on dichloro-tetrakis thiourea-nickel (DTN) [Soldatov et al., Phys. Rev. B 101, 104410 (2020)], a model of antiferromagnet on a tetragonal lattice with single-ion easy-plane anisotropy in the tilted external magnetic field is considered. Using the smallness of the in-plane field component, we analytically address field dependence of the energy gap in “acoustic” magnon mode and transverse uniform magnetic susceptibility in the ordered phase. It is shown that the former is non-monotonic due to quantum fluctuations, which was indeed observed experimentally. The latter is essentially dependent on the “optical” magnon rate of decay on two magnons. At magnetic fields close to the one which corresponds to the center of the ordered phase, it leads to experimentally observed dynamical diamagnetism phenomenon.

The electronic band structure of orthorhombic compound La₂CuO₄, which is the parent for a number of high-temperature superconductor families, has been calculated in terms of the density functional theory using the WIEN2k program package. Calculations have been performed by means of two exchange-correlation functionals. The former is a sum of the Tran- and Blaha-modified Becke–Johnson exchange potential and correlations in a local approximation, whereas the latter is the Perdew–Burke–Ernzerhof functional. Calculations taking into account spin polarization have shown the presence of an antiferromagnetic ground state in orthorhombic La₂CuO₄. Using the former functional, the magnetic moment of copper atoms and a semiconductor gap have been found to be M_Cu = 0.725μ_B and E_g = 2 eV. The latter has yielded M_Cu = 0.278μ_B and E_g = 0. Calculations results for the optical properties of orthorhombic La₂CuO₄: the electron energy losses, the real part of optical conductivity, and reflection coefficient, are in good agreement with experimental data. The calculated spatial distribution of the charge density in orthorhombic compound La₂CuO₄ has been analyzed with the aim of finding critical saddle points with parameters making it possible to classify the types of chemical bonds in crystals. The set of critical point parameters for orthorhombic La₂CuO₄ has turned out to be similar to that previously found by us for tetragonal La₂CuO₄ and related high temperature superconductors. In particular, the positive sign of the charge density Laplacian at bond critical points indicates the absence of covalent bonding in La₂CuO₄ according to the chemical bond classification proposed by Bader in his “Quantum Theory of Atoms in Molecules and Crystals.”

We present nonlinear dynamic equations for nematic and smectic A liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is expressed as a sum of external electric field, the fields originating from feedback of liquid crystal order parameter, and a field, created by charged impurities. The system tends to decrease the total electric field, because it lowers the energy density. This basically nonlinear problem is not a pure academic interest. In the realm of liquid crystals and their applications, utilized nowadays modern experimental techniques have progressed to the point where even small deviations from the linear behavior can be observed and measured with a high accuracy. We follow hydrodynamic approach which is the macroscopic description of condensed matter systems in the low frequency and long wavelength limit. Nonlinear hydrodynamic equations are well established to describe simple fluids. Similar approaches (with degrees of freedom related to the broken orientational or translational symmetry included) have been used also for liquid crystals. However to study behavior of strongly perturbed (well above the thresholds of various electro-hydrodynamic instabilities) liquid crystals, the nonlinear equations should include soft electromagnetic degrees of freedom as well. There are many examples of such instabilities, e.g., classical Carr-Helfrich instability triggered by the competitive electric and viscous torques, flexoelectric instability, and so one. Therefore the self-consistent derivation of the complete set of the nonlinear electro-hydrodynamic equations for liquid crystals became an actual task. The aim of our work is to present these equations, which is a mandatory step to handle any nonlinear phenomenon in liquid crystals.