Anisotropic<Emphasis Type="Italic">s</Emphasis>-wave or<Emphasis Type="Italic">d</Emphasis>-wave pairing? Analysis of experiments on ion irradiation of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-x</Subscript> films

The effect of ion irradiation on the superconducting transition temperatureT _c and resistivityρ _ab (T) of YBa₂Cu₃O_7-x films with different oxygen content (initial temperatureT _c0≈90 K and 60 K) is studied experimentally. The dependenciesT _c /T _c0 on residual resistivityρ _o are obtained in very wide range 0.2<T _c /T _c0 <1 andρ _o μΩ·cm. The critical values ofρ _o , corresponding to the vanishing of superconductivity, are found to be an order of magnitude larger then those predicted by theory ford-wave pairing. At 0.5÷0.6<T _c /T _c0<1 the experimental data are in close agreement with theoretical dependencies, obtained for the anisotropics-wave superconductor within the BCS-framework.     

Direct measurements of energy relaxation times on an AlGaAs/GaAs heterointerface in the range 4.2–50 K

The temperature dependence of the energy relaxation time τ_e (T) of a two-dimensional electron gas at an AlGaAs/GaAs heterointerface is measured under quasiequilibrium conditions in the region of the transition from scattering by acoustic phonons to scattering with the participation of optical phonons. The temperature interval of constant τ_e, where scattering by the deformation potential predominates, is determined. In the preceding, low-temperature region, where piezoacoustic and deformation-potential-induced scattering processes coexist, τ _e decreases slowly with increasing temperature. Optical phonons start to participate in the scattering processes at T∼25 K (the characteristic phonon lifetime was equal to τ_LOτ4.5 ps). The energy losses calculated from the τ_e data in a model with an effective nonequilibrium electron temperature agree with the published data obtained under strong heating conditions. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 371–375 (10 September 1996)     

On Pythagoras Theorem for Products of Spectral Triples

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes’ distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.     

Criteria for Separability of Multipartite Quantum System

We first present the Hamel base of the density operator space for multipartite quantum system, and thus establish a representation of density matrix. Moreover, according to the structure of the density matrix for multipartite quantum system, we present two necessary criteria for separability of multipartite quantum system of arbitrary dimensions.     

Electrical conductivity and band structure of thin polycrystalline EuS films

A study of the electrical resistance of thin polycrystalline EuS films (0.4–0.8 μm thick) in the temperature range 120–480 K has provided the basis for a model of the band structure of this substance. It has been shown that the main impurity levels in thin polycrystalline EuS films are those related with localized states near the conduction band bottom, as well as the E _i donor levels of Eu ions outside regular lattice sites. The “tail” of the localized states extends in energy up to at least ?0.45 eV.     

Numerical comparison of classical and permutation statistical hypothesis testing methods

The article is devoted to the classical problem of statistical hypothesis testing for the equality of two distributions. For normal distributions, Student’s test is optimal in many senses. However, in practice, distributions to be compared are often not normal and, generally speaking, unknown. When nothing is known about the distributions to be compared, one usually applies the nonparametric Kolmogorov–Smirnov test to solve this problem. In the present paper, methods are considered that are based on permutations and, in recent years, have attracted interest for their simplicity, universality, and relatively high efficiency. Methods of stochastic simulation are applied to the comparative analysis of the power of a few permutation tests and classical methods (such as the Kolmogorov–Smirnov test, Student’s test, and the Mann–Whitney test) for a wide class of distribution functions. Normal distributions, Cauchy distributions, and their mixtures, as well as exponential, Weibull, Fisher’s, and Student’s distributions are considered. It is established that, for many typical distributions, the permutation method based on the sum of the absolute values of differences is the most powerful one. The advantage of this method over other ones is especially large when one compares symmetric distributions with the same centers. Thus, this permutation method can be recommended for application in cases when the distributions to be compared are different from normal ones.     

Electronic structure and photoelectron spectra of nickel(II) acetylacetonate

Density functional theory and photoelectron spectroscopy are used to study the electronic structure of nickel acetylacetonate Ni(acac)₂. Based on the calculated energies and composition of the molecular orbitals and the pattern of localization of the electron density, the nature of the gas-phase photoelectron spectrum bands of Ni(acac)₂ is examined, and a new interpretation of it is proposed. The energies of the Kohn-Sham orbitals are assigned to the experimental vertical ionization energies in the approximation of the extended Koopmans theorem, which enables, with consideration given to the dependence of the Koopmans defect on the nature of the electronic level, to obtain a good agreement between the calculated orbital energies and experimental data on ionization energies.     

Relaxation and thermodynamic parameters of the theory of spin-wave damping in low-dimensional magnetic materials

Several basic parameters of the surface spectrum of a system are estimated with respect to the spin-spin interaction. An expression for the surface relaxation time and its numerical estimation are given. The dependence of the relaxation time on the geometric factor determined by the surface geometry only is presented. The conditions for the resonance absorption of spin-wave energy by the surface are considered. Certain expressions for the thermodynamic potentials taking the effect of surface resonance on the equilibrium properties of the system into account are given.     

Unsteady rarefied gas flow in a microchannel driven by a pressure difference

The kinetic S-model is used to study the unsteady rarefied gas flow through a plane channel between two parallel infinite plates. Initially, the gas is at rest and is separated by the plane x = 0 with different pressure values on opposite sides. The gas deceleration effect of the channel walls is studied depending on the degree of gas rarefaction and the initial pressure drop, assuming that the molecules are diffusely reflected from the boundary. The decay of the shock wave and the disappearance of the uniform flow region behind the shock wave are monitored. Special attention is given to the gas mass flux through the cross section at x = 0, which is computed as a function of time. The asymptotic behavior of the solution at unboundedly increasing time is analyzed. The kinetic equation is solved numerically by applying a conservative finite-difference method of second-order accuracy in space.