Spurious states of the dirac equation in a finite basis set

The occurrence of spurious states for the Dirac equation in a finite basis set is considered. For a Coulomb central-field potential, the spectra of the radial Dirac operator in a finite basis set (without using the kinetic balance) are shown to coincide for two different values of the relativistic quantum number κ that differ in sign. For an attractive Coulomb potential, this means that, for any basis set, spurious states p _1/2, d _3/2, … (κ > 0) arise, whose energies exactly coincide with energies of the states 1s _1/2, 2p _3/2, … (κ < 0), respectively. In addition, the negative spectra of the Dirac operator in a finite basis set for κ > 0 and κ < 0 also coincide.     

Magnetic field dependence of the thermal conductivity in EuxSr1-xS

The thermal conductivity κ of two Eu_xSr_1-x single crystals (x = 0.25 and 0.54) was measured between 1.5 and 25 K. In magnetic fields of ≈ 7 T κ is enhanced for temperatures up to 20 K with respect to κ(B = 0). At 1.5 K, where the relative increase κ(B)/κ(0) is largest, this ratio is 1.5 for x = 0.54 and ≈ 4 for x = 0.25. Two possible mechanisms for this effect, i.e. freezing of phonon scattering by magnetic excitations in a magnetic field, and heat transport by field-induced magnons, are discussed.     

The random lattice as a regularization scheme

A semi-analytic method to compute the first coefficients of the renormalization group functions on a random lattice is introduced. It is used to show that the two-dimensional O(N) nonlinear σ-model regularized on a random lattice has the correct continuum limit. A degree κ of “randomness” in the lattice is introduced and an estimate of the ratio Λ_random/Λ_regular for two rather opposite values of κ in the σ-model is also given. This ratio turns out to depend on κ.     

Magnetisation of type-II superconductors in the mixed state

The variational method, used in a previous work to study an isolated vortex tube, has been extended to calculate the magnetisation of type-II superconductors for arbitrary values of Ginzburg-Landau parameter κ and over the whole range of the magnetic field from hc₁ to hc₂. The results are discussed.     

On the basic states of one-dimensional disordered structures

The purpose of this paper is to study a limit probability distribution of the set of the first κ eigenvalues λ₁(?)<λ₂(?)<...<λ_κ(?) (with a fixed κ and ?→∞) of the boundary problem on the interval [0, ?] wherea(t, ω),q(t, ω) are the random stationary processes. Particularly the question of the repulsion between the first eigenvalues (small energetic levels) is studied. It has been proved that in the “divergent” case (q(t, ω)=0,a(t, ω)≠0) levels repulsion exists. As for the “potential” case (a(t, ω)≡1,q(t, ω)≠0) there is not any repulsion at all. This is one of the main differences between these two cases.     

On the possibility of direct measurement of the magnetic field-induced phase transition in hematite by means of magnetooptical method

It is shown that a rotation ? and a deformation κ of the optical indicatrix appear during the transverse magnetic field-induced phase transition in hematite. Analytic expressions for ? and κ are deduced from the magnetization-dependent electromagnetic energy in the crystal. It is shown that during the phase transition, induced by increasing the temperature, the electromagnetic energy in the crystal. It is shown that during the phase transition, induced by increasing the temperature, the antiferromagnetic vector L = M₁ - M₂ is rotating from the three-fold C₃ axis toward the basal plane, which implies that the main axis of the optical indicatrix is not aligned in a general case with the magnetic field or the crystallographic axis although the magnetic moment (M₁ + M₂) is always parallel to the field. The linear magnetic birefringence is very sensitive to the magnetic phase in hematite, as described in previous experimental work, but the present analysis shows that a direct determination of the transverse field-induced phase transition can be obtained in hematite, by means of a magnetooptical method, only when large and non-uniform rotation (up to ninety degrees) and variation of the shape of the indicatrix are taken into account.     

Departures from the Hauser-Feshbach theory due to the level-level correlations in deformed nuclei

A microscopic dynamical model is used for the inelastic scattering of nucleons by deformed nuclei and the fluctuation cross sections are calculated. The case of weak absorption in all channels is considered so that the number of statistical assumptions is minimized. The results are compared with the Hauser-Feshbach expressions as regards the magnitude and structure. The partial width amplitudes calculated from the model are correlated, the simplest type of level-level correlations being due to the similar-channels effect (SCE). When the correlations are due to SCE alone, the following two results are obtained, (i) The fluctuation cross sections are increased over the Hauser-Feshbach estimates, for Γ ? D and Γ ? D, by a factor κ if the entrance and exit channels are similar. The numerical value of κ is found to be 3 for a special case and in the general case it is conjectured to lie between the limits 1 and 3, (ii) The fluctuation cross sections σ_cc′^f1 and σ^f1_cc″ exhibit correlated fluctuations if the exit channels c′ and c″ are similar. The fluctuation cross sections in the cases “SCE+direct channel-channel coupling” and “SCE+intermediate structure” are also investigated. In all cases studied direct reaction cross sections do not vanish and the channelwise factorization assumption of the Hauser-Feshbach theory fails.     

RS model with a small curvature and dielectron production at the LHC

In the framework of the Randall-Sundrum-like scenario with the small curvature κ (RSSC model), p _⊥-distributions for the dielectron production at the LHC are calculated. For the summary statistics taken at 7 TeV (L = 5 fb^?1) and 8 TeV (L = 20 fb^?1), the exclusion limit on the 5-dimensional gravity scale M ₅ is found to be 6.35 TeV at 95% C.L. For √s = 13 TeV and integrated luminosity 30 fb^?1, the LHC search limit is estimated to be 8.95 TeV. These limits on M ₅ are independent of κ, provided the relation κ ? M ₅ is satisfied.     

The influence of rotatory inertia,tip mass,and damping on the stability of a cantilever beam on an elastic foundation

The stability of a uniform viscoelastic cantilever resting on an elastic foundation, carrying a tip mass, and subjected to a follower force at its free end is investigated. The effects of the rotatory inertia of the beam, the transverse and rotatory inertias of the tip mass, and the foundation modulus, which characterizes a Winkler type of elastic foundation, are included in the partial differential equation of motion and boundary conditions, and the influence of these quantities on the value of the critical flutter load parameter Q_f is sought. The exact forms of the fundamental frequency equations are derived for the cases of a viscoelastic and a purely elastic beam, and these equations are solved numerically for Q_f These numerical results reveal that Q_f depends strongly upon the foundation modulus for the cantilever carrying a tip mass or possessing rather small internal damping. In the absence of damping and a tip mass, the value of Q_f, computed upon the inclusion of the rotatory inertia of the beam in the formulation of the equation of motion, is decreased slightly and continues to decrease in essentially a linear manner as the value of the foundation modulus parameter κ is decreased. Moreover, when the effect of very small internal damping is included, the value of Q_f computed when the rotatory inertia of the beam is neglected increases slowly in an essentially linear fashion as x increases, whereas, when the effect of rotatory inertia is retained, the value of Q_f decreases as κ is increased. Additional numerical results are reported graphically.     

On the emergence of superconductivity and hysteresis in a cylindrical type I superconductor

One-dimensional vortex-free solutions of the system of Ginzburg-Landau equations (the so-called precursor states) are studied. These states describe the emergence of superconductivity in a long cylindrical type I superconductor, which was initially in the supercooled normal state in a magnetic field, and are formed upon subsequent reduction of the external field. The precursor states are responsible for the magnetic hysteresis in type I superconductors (for which κ < κ_c, where κ_c (R) is the critical value of the parameter κ in the Ginzburg-Landau theory, which is a function of radius). The range of fields is determined in which precursor states exist along with the Meissner state (and a hysteresis is possible) in the dependence of the cylinder radius R and parameter κ.     

Specific features of low-temperature phonon scattering in materials with tilted disclination loops

Phonon scattering by static stress fields of circular wedge disclination loops is investigated in the framework of the deformation potential approach. Numerical calculations of the mean free path l and thermal conductivity κ demonstrate that the temperature dependence of κ exhibits a minimum at a certain temperature T* in the low-temperature range. The thermal conductivity κ sharply increases as T ^?3 with a decrease in temperature (T<T*) and exhibits a dislocation behavior (κ ～ T ²) with an increase in temperature (T>T*). The results obtained for the wedge disclination loop are compared with the available data for uniaxial disclination dipoles. It is shown that the properties of uniaxial disclination dipoles serving as sources of phonon scattering are similar to those of wedge disclination loops.     

Zakharov equations with zeroth harmonic and a new type of modulation instability

It has been shown that the system of Zakharov equations for the amplitudes of the first and zeroth harmonics of the waves on the surface of an ideal liquid describes not only the known type of the modulation instability of the envelope of the main harmonic with respect to harmonic perturbations with small wave vectors κ (Benjamin-Feier modulation instability), but also the modulation instability of a combination of the main and zeroth harmonics at κ values on the order of the wave vector k ₀ of the main harmonic. In contrast to the Benjamin-Feier modulation instability typical for large depths, the described modulation instability does not disappear at k ₀ h < 1.363.     

Thermal conductivity and heat capacity of LuMgCu<Subscript>4</Subscript>

This paper reports on the measurements of the thermal conductivity κ and electrical resistivity ρ in the temperature range 5–300 K and the heat capacity at constant pressure C _p in the range 80–300 K for the metallic nonmagnetic compound LuMgCu₄. The experimental values of κ and C _p for the LuMgCu₄ compound are compared with the corresponding data available in the literature for the light heavy-fermion compound YbMgCu₄. It is shown that, in the low-temperature range (5–20 K), the phonon thermal conductivity κ_ph of YbMgCu₄ is lower than κ_ph of LuMgCu₄ as a result of phonon scattering from magnetic moment fluctuations of the Yb 4f electrons and, conversely, the heat capacity of LuMgCu₄ in the range 80–300 K is lower than that of YbMgCu₄ because the heat capacity of the latter compound has an additional magnetic component.     

Families of solutions to the generalized Ginzburg-Landau equation and structural transitions between them

Solutions to the generalized Ginzburg-Landau equations for superconductors are obtained for a Ginzburg-Landau parameter κ close to unity. The families of solutions with arbitrary number n of flux quanta in a unit cell are analyzed. It is shown that under certain conditions, a cascade of phase transitions between different structures in a magnetic field appears near T _c . Algebraic equations are derived for determining the boundaries of coexistence of different phases on the {T, H ₀} plane.     

Thermal conductivity of high-porosity biocarbon precursors of white pine wood

This paper reports on measurements of the thermal conductivity κ and the electrical conductivity σ of high-porosity (cellular pores) biocarbon precursors of white pine tree wood in the temperature range 5–300 K, which were prepared by pyrolysis of the wood at carbonization temperatures (T _carb) of 1000 and 2400°C. The x-ray structural analysis has permitted the determination of the sizes of the nanocrystallites contained in the carbon framework of the biocarbon precursors. The sizes of the nanocrystallites revealed in the samples prepared at T _carb = 1000 and 2400°C are within the ranges 12–35 and 25–70 Å, respectively. The dependences κ(T) and σ(T) are obtained for samples cut along the tree growth direction. As follows from σ(T) measurements, the biocarbon precursors studied are semiconducting. The values of κ and σ increase with increasing carbonization temperature of the samples. Thermal conductivity measurements have revealed that samples of both types exhibit a temperature dependence of the phonon thermal conductivity κ_ph, which is not typical of amorphous (and amorphous to x-rays) materials. As the temperature increases, κ_ph first varies proportional to T, to scale subsequently as ～T ^1.7. The results obtained are analyzed.     

Gauge parameter dependence in the background field gauge and the construction of an invariant charge

By using the enlarged BRS transformations we control the gauge parameter dependence of Green functions in the background field gauge. We show that it is unavoidable — also if we consider the local Ward identity — to introduce the normalization value ξ₀ of the gauge parameter ξ. The dependence of Green functions on ξ₀ is governed by a partial differential equation in a similar manner as the dependence on the normalization point κ is governed by the RG equation. By modifying the Ward identity we are able to construct in 1-loop order a gauge parameter independent combination of 2-point vector and background vector functions. By explicit construction of the next orders we show that this combination can be used to construct a gauge parameter independent RG-invariant charge. However, it is seen that this RG-invariant charge does not satisfy the differential equation of the normalization value ξ₀ of the gauge parameter, and, hence, is not ξ₀-independent as required.     

Isolated vortex structure and the lower critical field for clean type II superconductors far from Tc

The structure of an isolated vortex line and the lower critical field have been calculated numerically from Eilenberger's version of the Gorkov theory. Results for clean superconductors with κ between $\text{1}\text{√2}$and 2 and temperatures down to 0.25 T_c are reported and compared with experiment.     

Derivation of an optical potential for deuterons

A general interpolation scheme is described which allows to determine the different eigenvaluesE _n(κ) for a given value of κ by solving an eigenvalue problem of small rank. The elements of the corresponding matrix, not yet restricted by symmetry requirements, may be determined from calculated energy valuesE _n (κ) along the directions of high symmetry. In addition for different bands connected with one another a new set of Wannier functions is defined.     

Etude de grenats ferrimagnetiques d'yttrium substitues au scandium: Influence de la pression sur leur stabilite et leur temperature de curie

The garnets Y₃Fe₅O₁₂ and Y₃Fe_4.1Sc_0.9O₁₂ are unstable under high temperature and high pressure. They decompose into YFeO₃ and an iron oxide, usually Fe₃O₄. The high temperature decomposition is favoured by pressure and it spreads over a range of temperature which is larger for the substituted garnet than for the pure garnet. The experiments carried out on Y₃Fe₅O₁₂ corroborate the results of Marezio and Geller but do not show the existence of a dense form of this compound, in opposition to the conclusions presented by Shimada.The Curie temperature θ of the garnets Y₃Fe_5?xSc_x O₁₂ (x = 0,35, 0,70 and 0,90) has been measured under pressure up to 60 kbar. The Curie temperature increases under pressure according to the law θ_x (P) = θ_x (0)[ 1 + fP + hp²]. Thef and h coefficients are almost the same for the studied garnets and their average values are f = 2,07 · 10^?3kbar^?1andh = minus;8,37 · 10^?6kbar^?2. Our results are in agreement with what can be inferred from the theories of Geller and Rosencwaig. In addition, the law suggested by Bloch for the Néel ferrimagnetic compounds d Log θ/d Log $\text{V ? ?}\text{10}\text{3}$ can be also applied to these compounds.     

Thermal conductivity of a moderate heavy-fermion compound YbIn0.2Ag0.8Cu4

The thermal conductivity κ and electrical resistivity ρ of a cast polycrystalline sample of YbIn_0.2Ag_0.8Cu₄, which belongs to the class of moderate heavy-fermion compounds, are measured in the temperature range 5–300 K. It is shown that the phonon thermal conductivity of the sample follows an amorphous-like pattern throughout the temperature range covered, which should be assigned to the presence of Yb ions with a homogeneous mixed valence in this compound. The temperature dependence ρ(T) is divided into three portions: a high-temperature portion characteristic of conventional metals, a medium-temperature portion typical of Kondo compounds, and a low-temperature portion corresponding to a coherent Kondo lattice (the heavy-fermion regime). The Kondo temperature is estimated.