Anisotropy of the upper critical field and specific heat in V3Si — a superconductor with cubic symmetry

The specific heat of a V₃Si single crystal (T _c=17 K, H _c2=20 T) in magnetic fields up to 8 T isinvestigated experimentally for three orientations of the field relative to the crystallographic directions — H∥〈001〉, H∥〈110〉, and H∥〈111〉. Both the upper critical magnetic field and the specific heat of the mixed state are observed to depend on the orientation of the magnetic field relative to the crystallographic directions (anisotropy): The critical field reaches its maximum value and the specific heat its minimum value in a field along the 〈001〉 direction. The anisotropy scale in both phenomena increases as the magnetic field and reaches 3% in a 6 T field. The interrelationship of the upper critical field anisotropy and the specific-heat anisotropy in type-II superconductors is studied. It is shown that the anisotropy of the specific heat in the mixed state in weak fields can serve as a criterion for nontrivial pairing. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 26–29 (10 January 1999)     

Elastic magnetoimpurity resonance in diamond-like semiconductors (intravalley scattering)

The scattering by an excited neutral donor in Ge and Si near an energy-level crossing (on account of anisotropy of the effective mass) of the electronic states of the impurity as a function of the magnetic field is investigated. The crossing of the 2s-and 2p-like levels leads to the appearance of a nonzero dipole moment of the impurity atom and, therefore, a long-range potential, which is responsible for characteristic features in carrier transport. The transverse impurity conductivity is calculated. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 549–554 (25 October 1996)     

Investigation of low-temperature quantum diffusion in α-iron byμ + SR experiments on a single-crystal sphereSR experiments on a single-crystal sphere

The longitudinalμ ⁺-spin relaxation rate has been measured on a high-purity spherical α-iron single crystal at temperaturesT down to 20 mK and in applied magnetic fieldsB _appl parallel to 〈111〉 up to 3 T. Only above 1 K can the data be satisfactorily described by one rate constantГ. At 1 T≤B _appl≤2 T and 50 mK≤T≤300 mK, oscillations (“wiggles”) were in addition superimposed on the longitudinal relaxation. A qualitative understanding of the measurements may be achieved in terms of the increasing influence of internal stresses onμ ⁺ diffusion as the temperature is lowered.     

On Dynamics of 5D superconformal theories

5D superconformal theories involve vacuum valleys characterized in the simplest case by the vacuum expectation value of the real scalar field σ. If 〈σ〉 ≠ 0, conformal invariance is spontaneously broken and the theory is not renormalizable. In the conformally invariant sector 〈σ〉 = 0, the theory is intrinsically nonperturbative. We study classical and quantum dynamics of this theory in the limit when field dependence of the spatial coordinates is disregarded. The classical trajectories “fall” on the singularity at σ = 0. The quantum spectrum involves ghost states with negative energies unbounded from below, but such states fail to form complete 16-plets as is dictated by the presence of four complex supercharges and should be rejected for that reason. Physical excited states come in supermultiplets and have all positive energies.We conjecture that the spectrum of the complete field theory Hamiltonian also becomes positive definite (ghost-free) when invoking supersymmetry considerations.We speculate that the ghosts in higher derivative supersymmetric field theories are exterminated by a similar mechanism. The text was submitted by the author in English. On leave of absence from ITEP, Moscow, Russia     

The Landauer resistance of a one-dimensional metal with periodically spaced random impurities

We find the dependence of the ensemble-averaged resistance, 〈ρ _L〉, of a one-dimensional chain consisting of periodically spaced random delta-function potentials of the chain length L, the incident-electron energy, and the chain disorder parameter w. We show that generally the 〈ρ _L〉 vs L dependence can be written as a sum of three exponential functions, two of which tend to zero as L℩∞. Hence the asymptotic expression for 〈ρ _L〉 is always an exponential function of L. Such an expression for 〈ρ _L〉 means that the electronic states are indeed localized and makes it possible (which is important) to find the dependence of the localization radius on the incident-electron energy and the force with which an electron interacts with the sites of the chain. We also derive a recurrence representation for 〈ρ _L〉, which proves convenient in numerical calculations. Zh. éksp. Teor. Fiz. 111, 575–584 (February 1997)     

Statistical mechanics of braided Markov chains: I. Analytic methods and numerical simulations

We investigate numerically and analytically the statistics of Markov chains on so-called braid (B _n ) and locally free (ℒℱ _n ) groups. Namely, we compute the mean length 〈μ〉 and the variance 〈μ²〉−〈μ〉² of the shortest word which remains after applying of all group relations to the randomly generatedN-letter word (Markov chain). We express the conjecture (numerically justified) that the mean value 〈μ〉 for the random walk on the groupB _n (n≫1) coincides with high accuracy with the same value for the random walk on the “locally free group weth errors” if the number of errors is of order of 20%.     

Crystalline defect investigation based on electrons with characteristic energy losses

The features inherent to crystal point defect imaging based on electrons with characteristic energy losses are discussed. Variations in the contrast of a Si impurity atom as a function of its depth and the sample thickness, earlier obtained via numerical simulation, are analyzed by analytically solving the issue of multiwave dynamical diffraction along the Ge 〈100〉 direction at E = 300 keV.     

Polarization of leading Λ hyperons produced by neutrons on target nuclei

The polarization of the leading Λ hyperons produced on carbon and lead target nuclei by 4–10 GeV neutrons in the angle range Θ<8.5° with respect to the beam and with only neutral-particle accompaniment is measured: 〈Π〉=−0.096±0.018 for C and 〈Π〉=− 0.128±0.047 for Pb. The dependence of the polarization on the transverse momentum and the Feynman variable is measured. The normalized invariant cross section as a function of p _⊥ ² is found to be approximated by the function A exp(−Bp _⊥ ² ), where the parameter B is independent of the kind of nucleus (B=8.71±0.09 (GeV/c)⁻² for carbon and B=8.83±0.18 (GeV/c)⁻² for lead). Pis’ma Zh. éksp. Teor. Fiz. 64, No. 4, 237–240 (25 August 1996)     

Bell Inequalities as Constraints on Unmeasurable Correlations

The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations described by tree graphs. This implies classical representability of any set of correlations 〈A _i 〉, 〈B〉, 〈A _i B〉, and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for the unmeasurable correlation 〈A ₁ A ₂〉 associated to different choices for B. The same analysis applies to the Hardy model and to the “perfect correlations” discussed by Greenberger, Horne, Shimony and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical representation is the only basis for arguments about violations of locality and causality.     

Lattice mechanical properties of noble and transition metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the interatomic interactions, phonon dispersion curves (inq and r-space analysis), phonon density of states, mode Grüneisen parameters, dynamical elastic constants (C ₁₁,C ₁₂ andC ₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C ₁₂–C ₄₄), Poisson’s ratio (σ), Young’s modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y ₁), limiting value in the [110] direction (Y ₂), degree of elastic anisotropy (A), maximum frequencyω _max, mean frequency 〈ω〉, 〈ω ²〉^1/2=(〈ω〉/〈ω ⁻¹〉)^1/2, fundamental frequency 〈ω ²〉, and propagation velocities of the elastic constants in Cu, Ag, Au, Ni, Pd, and Pt. The contribution of s-like electrons is calculated in the second-order perturbation theory for the model potential while that of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has proved the ability of our model potential for predicting a large number of physical properties of transition metals.     

Dependence of the frequencies of magnetostatic waves on the magnetizing field in ferrite films

Analytical expressions are derived for the derivatives of the frequencies of magnetostatic waves with respect to the external magnetic field in anisotropic ferromagnetic films. Films having cubic anisotropy and 〈100〉, 〈110〉, and 〈111〉 surfaces are analyzed in detail. The frequency-field relations are used in an experimental determination of the temperature coefficients of the cubic anisotropy field and the saturation magnetization in an yttrium iron garnet film. Fiz. Tverd. Tela (St. Petersburg) 40, 2089–2092 (November 1998)     

Intervalley scattering in GaAs: ab initio calculation of the effective parameters for Monte Carlo simulations

Interactions between excited electrons and short-wavelength (intervalley) phonons in GaAs are studied using density functional theory for the conduction bands, and density functional perturbation theory for phonon frequencies and matrix elements of the electron–phonon interaction. We have calculated the deformation potentials (DPs) and the average intervalley scattering time 〈τ〉. The integration of the scattering probabilities over all possible final states in the Brillouin zone has been performed without any ad hoc assumption about the behavior of the electron–phonon matrix elements nor the topology of the conduction band. For transitions from the L point to Γ valley (within the first conduction band), we find 〈τ〉_L to be 1.5 ps at 300 K, in good agreement with time-resolved photoluminescence experiment. We discuss the difference between our calculated DPs, and effective parameters used in Monte Carlo simulations of optical and transport properties of semiconductors. The latter are based on Conwell’s model, in which electron–phonon interaction is described by one single constant and a parabolic model is used for conduction bands. We deduce the effective DP from our 〈τ〉, and compare it to our calculated DPs. We conclude that only effective DPs obtained from a full calculation of 〈τ〉 are relevant parameters for Monte Carlo simulations. PACS 71.10-w; 72.10.Di; 71.55.Eq     

Wave mechanics of two hard core quantum particles in A 1-D box

The wave mechanics of two impenetrable hard core particles in a 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a macro-orbital (a kind of pair waveform). While the expectation value of their interaction, 〈 V _HC (x) 〉, vanishes for every state of two particles, the expectation value of their relative separation, 〈 x 〉, satisfies 〈 x 〉≥λ/2 (or q ≥ π/d, with 2d=L being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with 〈 x 〉= λ/2, phase position separation Δϕ = 2π and momentum |q _o| = π/d) and experience a mutual repulsive force (zero point repulsion) f _o =h ²/2md ³ which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining a correct microscopic understanding of widely different many-body systems.     

Orientation dependence of electrical properties of 0.96Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript>-0.04BaTiO<Subscript>3</Subscript> lead-free piezoelectric single crystal

In this paper, a single crystal of 0.96Na_0.5Bi_0.5TiO₃-0.04BaTiO₃ with dimensions of Φ 30×10 mm was grown by the top-seeded-solution growth method. X-ray powder diffraction results show that the as-grown crystal possesses the rhombohedral perovskite-type structure. The dielectric, piezoelectric and electrical conductivity properties were systematically investigated with 〈001〉, 〈110〉 and 〈111〉 oriented crystal samples. The room-temperature dielectric constants for the 〈001〉, 〈110〉 and 〈111〉 oriented crystal samples are found to be 650, 740 and 400 at 1 kHz. The (T _m, ε _m) values of the dielectric temperature spectra are almost independent of the crystal orientations; they are (306°C, 3718), (305°C, 3613) and (307°C, 3600) at 1 kHz for the 〈001〉, 〈110〉 and 〈111〉 oriented crystal. The optimum poling conditions were obtained by investigating the piezoelectric constants d ₃₃ as a function of poling temperature and poling electric field. For the 〈001〉 and 〈110〉 crystal samples, the maximum d ₃₃ values of 146 and 117 pC/N are obtained when a poling electric field of 3.5 kV/mm and a poling temperature of 80°C were applied during the poling process. The as-grown 0.96Na_0.5Bi_0.5TiO₃-0.04BaTiO₃ crystal possesses a relatively large dc electrical conductivity, especially at higher temperature, having a value of 1.98×10⁻¹¹ Ω⁻¹⋅m⁻¹ and 3.95×10⁻⁹ Ω⁻¹⋅m⁻¹ at 25°C and 150°C for the 〈001〉 oriented crystal sample.     

Realization of a heavily doped and fully compensated semiconductor state in a crystalline semiconductor with a deep impurity band

We use the data on the pressure (up to P=1.5 GPa) and field (up to H=17 kOe) dependence of the Hall coefficient and the resistivity at 77.6 and 300 K in p-CdSnAs₂〈Cu〉 to calculate the effective kinetic characteristics of the charge carriers, the density and mobility of the conduction electrons and the holes of the deep acceptor and valence bands, in an interval of excess-acceptor densities N _ext ranging from 10¹⁰–10¹⁷ cm⁻³. We establish that in a heavily doped semiconductor with a deep impurity band at the tail of the density of states of the intrinsic band, with unequal donor and acceptor densities, a a heavily doped and fully compensated semiconductor state is realized under hydrostatic compression. The threshold value of the pressure that initiates the transition into such a state, P _c, depends on the extent to which the impurity band is populated. In p-CdSnAs₂〈Cu〉 at N _ext=N _A, where N _A is the density of deep acceptors, and T⩽77.6 K the value of P _c amounts to 10⁻⁴ GPa. As the population of the deep acceptor band grows, P _c increases and in the limit becomes infinite. We discuss the special features of the electrophysical properties of p-CdSnAs₂〈Cu〉 arising from the absence of an energy gap between the states of the conduction band and those of the deep acceptor band. Zh. éksp. Teor. Fiz. 111, 562–574 (February 1997)     

Using the full Raman depolarisation in the determination of the order parameters in liquid crystal systems

The depolarisation ratio for the Raman-active phenyl stretching mode has been measured over the whole of the mesophase range, and the orientational order parameters deduced, in the uniaxial nematic liquid crystal octylcyanobiphenyl (8CB). Linearly polarised light was incident normally on a homogeneously aligned sample and a χ² minimisation routine performed on the 360^° depolarisation ratio profile. The order parameters 〈P ₂₀₀〉 and 〈P ₄₀₀〉 , together with the differential polarisability ratio, r , are used as fitting parameters and measured as a function of temperature. Interestingly, we show that the value for r , conventionally measured in the isotropic phase and assumed to remain constant, has a clear temperature dependence, ranging from -0.032±0.008 in the isotropic phase through to -0.245±0.015 at the nematic-to-smectic A phase transition. The measured order parameters 〈P ₂₀₀〉 and 〈P ₄₀₀〉 varied from 0.35- 0.55±0.02 and 0.180- 0.245±0.02 , respectively, across the 8 ^° C wide nematic phase range. The values of both 〈P ₂₀₀〉 and 〈P ₄₀₀〉 are in excellent agreement with theory, but it is noteworthy that 〈P ₄₀₀〉 shows a much better quantitative match than has been reported in previous work. Crucially the temperature dependence of r is shown to be a contributing factor in the low 〈P ₄₀₀〉 values that have been conventionally reported from Raman scattering measurements. The potential for fitting the entire angular depolarisation ratio distribution in liquid crystalline systems that are described by more order parameters, specifically biaxial materials, is discussed.     

Large-scale amplification of a magnetic field by turbulent helicity fluctuations

In this paper the procedure of large-scale averaging of the magnetic-field diffusion equation with the α-term curlα(r,t)B(r,t) is used to show that a nonuniform distribution of the turbulent helicity fluctuations (more precisely, the fluctuations of the coefficient α) with a zero average value gives rise to large-scale amplification of the initial magnetic field. A detailed study is carried out of the dependence of the resulting large-scale α effect on the characteristics of the correlator 〈〈α(r, t)α(r″,t″)〉〉 in a rotating medium with a nonuniform distribution of the angular velocity ω=ω(ρ,z) (ρ is the distance for the rotation axis z). The effect of helicity fluctuations and the diffusion coefficient on the turbulent diffusion process is also investigated. Zh. éksp. Teor. Fiz. 116, 85–104 (July 1999)     

Extremum uncertainty product and sum states

We consider the states with extremum products and sums of the uncertainties in non-commuting observables. These are illustrated by two specific examples of harmonic oscillator and the angular momentum states. It shows that the coherent states of the harmonic oscillator are characterized by the minimum uncertainty sum 〈(Δq)²〉 + 〈(Δp)²〉. The extremum values of the sums and products of the uncertainties of the components of the angular momentum are also obtained.     

Observation of spin-reduction anisotropy in the quasi-one-dimensional antiferromagnet CsMnI3

The NMR of ⁵⁵Mn in the quasi-one-dimensional noncollinear antiferromagnet CsMnI₃ at T=1.3 K is investigated in magnetic fields up to ∼40 kOe. Six NMR branches corresponding to six manganese spins per magnetic unit cell are observed. The NMR spectra correspond satisfactorily to the well-known magnetic structure of CsMnI₃, taking into account the dynamic frequency shift due to the interaction with the low-lying AFMR modes. The average spins 〈S _A〉=1.86 and 〈S _B〉=1.74 of the magnetically nonequivalent Mn²⁺ ions are determined from the measured values of the hyperfine fields. The results obtained agree qualitatively with the calculations of spin reduction in quasi-one-dimensional antiferromagnets [Y. Watabe, T. Suzuki, and Y. Natsume, Phys. Rev. B 52, 3400 (1995)]. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 661–665 (10 May 1998)     

Double-beta decay: Present status

The present status of double-beta-decay experiments (including the search for 2β ⁺, ECβ ⁺, and ECEC processes) are reviewed. The results of the most sensitive experiments are discussed. Average and recommended half-life values for two-neutrino double-beta decay are presented. Conservative upper limits on effective Majorana neutrino mass and the coupling constant of the Majoron to the neutrino are established as 〈m _ν 〉 < 0.75 eV and 〈g _ee 〉 < 1.9 × 10⁻⁴, respectively. Proposals for future double-betadecay experiments with a sensitivity for the 〈m _ν 〉 at the level of 0.01–0.1 eV are considered.