For bosons and fermions a new representation of the Hamilton operator corresponding to creation and annihilation of clusters is given. The obtained principle of correspondence between symbols and operators allows us to quantize the entropy and free energy. The minimal value of the quantum free energy in the thermodynamical limit matches the classical free energy. An estimate of this minimal value for a boson system with strong interaction, where the phase transition to superfluidity is possible, is presented.
Show AbstractA problem of finding the excited states wave functions of quantum systems with additional integrals of motion in the classical limit has been considered. Recurrence relations determining wave functions accurate to within a normalization factor for a certain range of values of interaction potential parameters have been obtained.
Show AbstractGenerating sections of conservation laws for the elliptic Liouville equation are constructed. It is shown that a nontrivial conservation law corresponds to any generating section and demonstrated that all classical conservation laws arise from the Lagrangian symmetries. Explicit formulas for the development of a certain conservation law by its generating section are obtained.
Show AbstractA mathematical model of the polarized radiation scattering by an axially asymmetric structure placed under a film on a permeable substrate is developed. Results on scattering by variously shaped particles are presented.
Show AbstractThe basis property of the system of root vectors for a cylindrical waveguide with a circular cross section and dielectric filling is substantiated. This lays the grounds for applying the normal wave method to the waveguide excitation problem.
Show AbstractAn integral transformation method is used to find the energy spectrum of the radial Schr$\stackrel{..}{o}$dinger equation with an infinitely increasing power-law confining potential. The problem is reduced to an approximate solution of an infinite system of linear algebraic equations. Numerical computations are used to determine the $S$-state spectrum of the Schr$\stackrel{..}{o}$dinger equation with a linearly increasing potential.
Show AbstractA three-dimensional mathematical model of the dielectric deflector with electrooptical control is considered. A method for calculating the electric field inside the deflector crystal, which adequately takes into account the shape of electrodes, is proposed. The area of application of the earlier developed model is investigated.
Show AbstractAn explicit solution to the boundary-value problem for a harmonic function outside a cut lying on a circle arc has been constructed. The Dirichlet condition is specified on one bank of the cut, the Neumann condition, on the other bank. The solution of the problem is based on reducing it to the Riemann-Gilbert problem.
Show AbstractAn experimental system for studying the most energetic cosmic rays is described, which can be installed on board the Russian segment of the International Space Station.
Show AbstractBased on the real energy spectrum and wave function of the Tm-ion in the vanadate crystal field, all strain susceptibilities and the $\Delta E$ effect were calculated. A good description of the $C^{\delta}(T)$ and $C^{\gamma}(T)$ experimental elastic constants and their variations in magnetic field in the tetragonal and rhombic phases was obtained. The $B^{\delta}$ and $B^{\gamma}$ magnetoelastic and $K^{\delta}$ and $K^{\gamma}$ pair quadrupole coefficients were determined. The influence of the magnetic field oriented along various symmetrical directions in the crystal on the quadrupole ordering in TmVO$_{4}$ was studied.
Show AbstractWithin the framework of the Landau phenomenological model, the temperature and sample-thickness dependences of the heat capacity of thin uniaxial ferroelectric films near the second-order phase transition were studied. The heat capacity jump was found to decrease, diffuse, and shift to lower temperatures as the thickness of thin films decreased. At a certain thin-film thickness, the heat capacity anomaly disappeared (for instance, for triglycine sulfate, at a thickness of several nanometers).
Show AbstractA new and simple approach to the space ergodicity problem is suggested. By averaging along an arbitrary horizontal straight line rather than by volume averaging, the spatial statistical characteristics of the phase of a wave normally incident on a randomly inhomogeneous plane-layered medium are obtained. In that case (in contrast to volume averaging), the regular wave properties are not masked. It is demonstrated that the spatial stochastic characteristics can be determined from time-average measurements only when the medium inhomogeneities drift at a constant horizontal velocity.
Show AbstractBased on the analysis of field measurement results, the evolution of the bottom density current in wind strengthening has been revealed. The measured and calculated flow velocity distributions have been compared. It has been found that the inn.er wave induces the momentum transfer from the drift flow to the bottom one. Semiempirical expressions for the characteristics of this process accounting for the effect of pressure gradient and density stratification on the current have been obtained.
Show AbstractA special perturbation function expansion in the three-body problem for orbital resonances in the case of large eccentricities is substantiated. The given expansion can be used to construct an analytical solution allowing the orbital evolution of asteroids and comets to be interpreted.
Show AbstractA new method for obtaining a stable surface microwave discharge in the boundary layer at a dielectric body streamlined by a supersonic air flow, which can be replicated in various experiments, is suggested. The main plasma parameters of such a discharge are determined.
Show AbstractThe semiclassical size effect is shown to substantially affect the optical and magnetooptical spectra of ferromagnetic granular alloys. In particular, a decrease in the size of granules can cause changes in the amplitude, profile, and sign of the equatorial Kerr effect.
Show AbstractThe results of model experiments on the study of the structure of intense convective air vortices are presented. The influence of the underlying surface temperature on the temperature and humidity field and on the maximum value of the horizontal velocity component in the vortex is considered.
Show Abstract
