Transformation of the effective rotational Hamiltonian of nonrigid X 2 Y molecules

The transformation of the effective rotational Hamiltonian H of nonrigid X ₂ Y molecules to the form having a minimum number of diagonals in the basis of rotational functions of a symmetric top is discussed. Such a transformation is a generalization of the reduction transformation performed for the polynomial effective Hamiltonian H. It is shown that in the general case the transformation substantially changes the form of the initial Hamiltonian, which restricts the region of applicability (J<J*) of the reduced Hamiltonian represented in a class of elementary functions in terms of angular momentum operators. The values of the rotational quantum number J* are estimated for the (000) ground and (010) vibrational states of the H₂O molecule.     

Optimal oscillation-center transformations

Systems with Hamiltonians of the form H₀(p) + H₁(q,p,t) are considered. A variational principle is proposed for defining that canonical transformation, continuously connected with the identity transformation, which minimizes the residual, coordinate-dependent part of the new Hamiltonian. The principle is based on minimization of the mean square generalized force over phase space and time. The transformation reduces to the action-angle transformation in that part of the phase space of an integrable system where the orbit topology is that of the unperturbed system, or on primary KAM surfaces. General arguments in favour of this definition are given, based on Galilean invariance, decay of the Fourier spectrum, and its ability to include external fields or inhomogeneous systems. The optimal oscillation-center transformation for the physical pendulum (or particle in a sinusoidal potential) is constructed analytically. A modified principle for relativistic systems is presented in an appendix.     

Metal-insulator transition in hydrogen and in expanded alkali metals

Two methods are considered for testing the stability of an electron gas to formation of bound states round a pair of protons. In the first, the screened potential for the two protons is set up as a superposition, which is appropriate in a very high density electron gas. The condition for bound state formation is then examined in the two-centre problem. The density thus obtained is in the right density range to accord with the experiment of Hawke et al. for producing cold metallic hydrogen.This has encouraged us to attempt a more ambitious calculation, namely the investigation of the Heitler-London energy of a model H₂ molecule with screened electron-nuclear and electron-electron interactions, the screening being again through appropriate introduction of the Thomas-Fermi screening radius. The merit of this second model is that the theory contains the Heitler-London value of the dissociation energy of the free H₂ molecule in the limit when the density of the electron gas tends to zero. This feature, the binding energy of the diatomic and its importance in distinguishing the metal-insulator transition in hydrogen from those expected to occur in expanded alkali metals is stressed. The second point we stress is that, in both the models discussed above, there is a close connection with the one-centre criterion for bound state formation. Though we have not carried out detailed two-centre calculations for expanded alkali metals, nevertheless some discussion is given of the one-centre bound state criterion in these metals.Some remarks are also made on the dielectric function of molecular crystals, in relation to the insulator-metal transition.     

Complex singularity of a stokes wave

Two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth can be described by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave propagating with the constant velocity. The increase in the scaled wave height H/λ from the linear limit H/λ = 0 to the critical value H _max/λ marks the transition from the limit of almost linear wave to a strongly nonlinear limiting Stokes wave. Here, H is the wave height and λ is the wavelength. We simulated fully nonlinear Euler equations, reformulated in terms of conformal variables, to find Stokes waves for different wave heights. Analyzing spectra of these solutions we found in conformal variables, at each Stokes wave height, the distance ν _c from the lowest singularity in the upper half-plane to the real line which corresponds to the fluid free surface. We also identified that this singularity is the square-root branch point. The limiting Stokes wave emerges as the singularity reaches the fluid surface. From the analysis of data for ν _c → 0 we suggest a new power law scaling ν _c ∝ (H _max ? H)^3/2 as well as new estimate H _max/λ ? 0.1410633.     

Magnetization reversal dependence on magnetic properties of a spin torque oscillator with in-plane anisotropy free layer and orthogonal polarizer

The effect of magnetic properties on magnetization dynamics is studied for a spin torque oscillator (STO) composed of a free layer with an in-plane magnetic anisotropy and a reference layer with a fixed out-of plane magnetization. A transition from damped to uniform oscillations is observed for a critical value of saturation magnetization M_S). In the uniform oscillations regime, the frequency is inversely proportional to M_S. Similarly, the critical current for achieving uniform oscillations is investigated as a function of free layer intrinsic properties. In a second part of the study, the magnetostatic field (H_m) from the reference layer is considered and it is revealed that the out-of plane component of magnetization has a strong dependence on H_m. For a particular configuration, H_m could reduce the out-of plane component maximizing thus the out-put signal of the STO.     

The initial stage in the nonlinear motion of a domain wall in garnet films

A study of the domain-wall motion in single-crystal garnet films of the YBiFeGa system with a perpendicular magnetic anisotropy, activated by a constant in-plane bias field H _p parallel to the wall plane and a pulsed drive field H _g of an amplitude corresponding to the nonlinear region of the domain-wall velocity vs. the H _g relation is reported. The earlier data suggesting the existence of an initial phase of motion, where the wall is accelerated to a high instantaneous velocity, have been confirmed. The wall behavior in the initial phase has been shown to be affected by the field H _p and the drive-field pulse rise time. A possible mechanism of the wall structure transformation after the application of the H _g pulse is considered. It has been established that the dependence of the wall velocity on H _p in the saturation region disagrees with theory.     

Low-field irreversibility line and its anisotropy of textured (Bi,Pb)2Sr2Ca2Cu3Oy silver-clad tapes

The irreversibility line H_irr(T) of textured (Bi,Pb)₂Sr₂Ca₂Cu₃O_y silver-clad tapes was obtained by ac susceptibility (ACS) and magnetoresistivity (MR) below 1500 G. It is found that, in the framework of flux motion, the H_irr(T) is determined by the thermally activated flux flow (TAFF) rather than the so-called giant flux creep, and the experimentally obtained H_irr(T) line is related to a certain resistivity criterion in both ACS and resistivity measurements. H_irr(T) is found to be significantly depressed by the amplitude of applied driving AC field and generally lower than that measured from the resistivity. The anisotropy in H_irr(T) is found to follow a scaling behaviour as described by the anisotropic effective mass model.     

Upper critical fieldH c3 of superconductors for all electron mean free paths

In this paper the ratioH _c3/H _c2 is calculated for all electron mean free paths. Correction terms to the standard resultH _c3/H _c2=1,695 are obtained both in the Ginzburg-Landau region and in the dirty limit at all temperatures. In the clean limit our results are identical with those obtained earlier byLüders.     

The solution of Hydrogen in TaV2

TaV₂ may be prepared as a random b.c.c. alloy or as a (C-15) Laves phase. The behavior of hydrogen dissolved in b.c.c. TaV₂ is significantly different than that exhibited by hydrogen dissolved in (C-15) TaV₂. The b.c.c. TaV₂/H₂; system is similar to pure vanadium/H₂; in the region of hydrogen solid solution, the electronic contribution to the thermodynamics of solution is negligible and the system exhibits apparent H-H attractive interactions. A non-stoichiometric f.c.c. dihydride is formed at p_H2 = 10 atm, T = 273 K. (C-15) TaV₂ does not form a hydride phase; hydrogen is continuously absorbed into solid solution to a maximum hydrogen content H/M ? 0.60. The solid solution of hydrogen in (C-15) TaV₂ exhibits trends which are typical of intermetallie/H₂ systems. The dilute hydrogen region is marked by a strong positive deviation from Sieverts' Law, and the relative partial molar enthalpy of solution becomes less exothermic as the hydrogen content is increased. ΔV? vs H/M relationships and ΔS_H vs H/M relationships indicate that hydrogen segregation at the metal surface or at abnormally stable trapping sites does not contribute significantly to the thermodynamic behavior exhibited by hydrogen in (C-15) TaV₂. Analysis of the excess free energy of hydrogen suggests that electronic effects may exert a significant influence on the behavior of hydrogen in (C-15) TaV₂, even at dilute hydrogen contents. It is suggested that the radom substitution of tantalum into the vanadium lattice exerts a significantly greater effect on the vibrational entropy of dissolved hydrogen than does the structural transformation b.c.c. TaV₂ → (C-15) TaV₂.     

A positive energy dynamics and scattering theory for directly interacting relativistic particles

Starting from the tensor product of N irreducible positive energy representations of the Poincaré group describing N free relativistic particles with arbitrary spins and positive masses, we construct an interacting positive energy representation by modifying the total 4-momentum operator. We first make a transformation to a Hilbert space on which the free total 4-momentum operator equals the product of a dimensionless center-of-mass 4-vector ($\text{(|k|}{}^2\text{+ 1)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, k) and a free “reduced Hamiltonian” H_r⁰, which is a positive operator acting only on internal variables, and then replace H_r⁰ by an interacting reduced Hamiltonian H_r = H_r⁰ + V, where V commutes with the Lorentz group and is such that H_r is a positive operator. The resulting product form is shown to imply that the wave operators interwine the free and interacting representations so that the S-operator is Lorentz invariant. From a physical point of view the scheme is related to the framework first introduced by Bakamjian and Thomas, in which the Hamiltonian and boost generators are modified, but the above procedure makes a mathematically rigorous discussion much simpler. In the spin-zero case we introduce a natural generalization of the pair potentials of nonrelativistic N-particle Schrödinger theory to the present relativistic setting, study its scattering theory, and point out some problems that do not have analogs at the nonrelativistic level. In the $\text{spin}\text{-}\text{1}\text{2}$ case we propose, inspired by the Dirac equation, explicit reduced Hamiltonians to describe atomic energy levels and present arguments making plausible that their eigenvalues are in closer agreement with the experimental data than their nonrelativistic counterparts. We also consider extensions to arbitrary spin and, in the $\text{spin}\text{-}\text{1}\text{2}$ case, coupling of a quantized radiation field. In view of eventual applications to “completely integrable” one-dimensional field theories the case of one space dimension is studied as well, both in quantum mechanics and in classical mechanics.     

Structural transformation of the oxygen and proton conductor Ba2In2O5 in humid air: an in-situ X-ray powder diffraction study

The oxygen and proton conductor Ba₂In₂O₅ is known to undergo a structural transformation in humid atmosphere at about 300°C. The resulting phase Ba₂In₂O₅·H₂O was investigated by in-situ high-temperature X-ray diffraction. During the transformation, a transient structure existing near 320°C in a narrow temperature interval is formed. Ba₂In₂O₅·H₂O is stable from ≈300°C down to room temperature and may be characterized by S.G. P4/mmm, No. 123, tetragonal, with a=4.1827(10) Å, b=4.1827(10) Å and c=8.9617(10) Å. The atomic rearrangement during the transformation together with the change of the coordination of one half of the In atoms from tetrahedral to octahedral symmetry reduces the unit cell volume of Ba₂In₂O₅·H₂O to one quarter of the initial value. Linear thermal expansion coefficients of both phases show a strong anisotropy.     

Free energy in the (2+1)-dimensional SU(2) QCD model against the background of a gauge-field condensate

The thermodynamic potential (free energy) for quarks and gluons in (2+1)-dimensional spacetime is calculated in the one-loop approximation at finite temperatures against the background of a constant uniform color magnetic field H and a constant uniform A ₀ condensate. The problem of interpreting the tachyon mode in the gluon energy spectrum is discussed. The question of whether the free energy may develop a minimum at nonzero values of H and A ₀ is analyzed.     

Shape and size transformation of gold nanorods (GNRs) via oxidation process: A reverse growth mechanism

The anisotropic shape transformation of gold nanorods (GNRs) with H₂O₂ was observed in the presence of “cethyl trimethylammonium bromide” (CTAB). The adequate oxidative dissolution of GNR is provided by the following autocatalytic scheme with H₂O₂: Au⁰ → Au⁺, Au⁰ + Auⁿ⁺ → 2Au³⁺, n = 1 and 3. The shape transformation of the GNRs was investigated by UV-vis spectroscopy and transmission electron microscopy (TEM). As-synthesised GNRs exhibit transverse plasmon band (TPB) at 523 nm and longitudinal plasmon band (LPB) at 731 nm. Upon H₂O₂ oxidation, the LPB showed a systematic hypsochromic (blue) shift, while TPB stays at ca. 523 nm. In addition, a new emerging peak observed at ca. 390 nm due to Au(III)-CTAB complex formation during the oxidation. TEM analysis of as-synthesised GNRs with H₂O₂ confirmed the shape transformation to spherical particles with 10 nm size in 2 h, whereas centrifuged nanorod solution showed no changes in the aspect ratio under the same condition. Au³⁺ ions produced from oxidation, complex with excess free CTAB and approach the nanorods preferentially at the end, leading to spatially directed oxidation. This work provides some information to the crystal stability and the growth mechanism of GNRs, as both growth and shortening reactions occur preferentially at the edge of single-crystalline GNRs, all directed by Br⁻ ions.     

Solution of the problem of indirect spin-spin interaction via the phonon field

A new transformation which differs from the famous one of Fröhlich is introduced to transform the hamiltonian of the interacting spin system and phonon system to a representation which leads to the exact expression for the operator H_SS of the indirect spin-spin interaction via the phonon field. The evident form of the operator H_SS is determined.     

90° pulsed magnetization of ferrite-garnet films with easy-plane anisotropy

The process of pulsed 90° magnetization of ferrite-garnet films was studied. These films, in addition to easy-plane anisotropy, have biaxial anisotropy in the film plane with an effective field H _K2 ? 40–55 Oe. the pulsed magnetization curve contains two portions separated by a kink observed at a field pulse amplitude H _p=H _p ^* ? 16–18 Oe. An analysis of the magnetization signals showed that the restoring torque, which is mainly caused by biaxial-anisotropy forces, is overcome in fields H _p ≥ H _p ^* and that magnetization rotation occurs. In fields H _p < H _p ^* , the magnetization vector rotates at the initial stage only and the angle of rotation ?_in is less than 25°–26°. The field H _p ^* and angle ?_in are calculated. The results of the calculations are confirmed by experimental data. In fields H _p > H _p ^* , the process of magnetization is accompanied by oscillations of the magnetization vector. In contrast to free magnetization oscillations, these oscillations are nonlinear and the frequency of the first harmonic (≈5 × 10⁸ Hz) is much lower than that for free oscillations, (7–12) × 10⁸ Hz. Oscillations are excited at a pulse rise time of ≈6 ns.     

Influence of hydrogen on structural and magnetic properties of the hexagonal Laves phase HoMn2

The HoMn₂ compound crystallizes in the cubic C15 or hexagonal C14 Laves phases depending on preparation. The effect of hydrogen absorption on structural and magnetic properties of HoMn₂H_x hydrides for the C14 phase has been investigated by XRD and AC/DC magnetometry in the temperature ranges of 75-380 K and 4-390 K, respectively. In addition to general features revealed by RMn₂H_x compounds (R=rare earth or Yttrium), unusual behavior of these hydrides was found. In particular, a transformation from the hexagonal to the monoclinic structure was detected, the same as that observed for cubic HoMn₂H_x compounds. The structural transformations are correlated to the magnetic behavior. The presented results are compared mainly with the properties of the cubic HoMn₂H_x hydrides as well as with those of other RMn₂H_x hydrides. Tentative magnetic and structural phase diagrams are proposed.     

Hydrogen indium vacancy complex VInH4 in n-type InP studied by positron-lifetime

Positron-lifetime experiments have been carried out on two undoped n-type liquid encapsulated Czochralski (LEC)-grown InP samples with different stoichiometric compositions in the temperature range 10-300 K. For temperatures below 120 K for P-rich InP and 100 K for In-rich InP, the positron average lifetime began to increase rapidly and then leveled off, which was associated with the charge state change of hydrogen indium vacancy complexes from (V_InH₄)⁺ to (V_InH₄)⁰. This phenomenon was more obvious in P-rich samples that have a higher concentration of V_InH₄. The transformation temperature of approximately 120 K suggests that the complex V_InH₄ is a donor defect and that the ionization energy is about 0.01 eV. The ionization of neutral V_InH₄ accounted for the decrease of the positron average lifetime when the sample was illuminated with a photon energy of 1.32 eV at 70 K. These results provide evidence for hydrogen complex defects in undoped LEC InP.     

Dirac dynamics on stochastic phase spaces for spin 1/2 particles

The Foldy-Wouthuysen representation of the dynamics of a free spin $\text{1}\text{2}$ particle is formulated in a Hilbert space $\text{H}$(Γ) of spinor-valued functions over Γ-space. $\text{H}$(Γ) carries a reducible Wigner-type representation of the Poincaré group. The transition to the Dirac representation in a new bispinor Hilbert space $\text{K}$(Γ) is effected by means of a generalized inverse Foldy-Wouthuysen transformation. Explicit expressions are derived for the resolution generators η of invariant subspaces $\text{K}$±(Γ_η) carrying irreducible representations of the resulting representations of the Poincaré group. The formalism is recast in a manifestly covariant form and the Dirac equation on $\text{H}$(Γ_s) with minimal coupling to a four-potential is examined. It is shown that the resulting external field theory is gauge-invariant and relativistically covariant.     

Metamagnetic model in a field of arbitrary direction

The free energy of a metamagnetic model, in a magnetic field making an angle θ with the direction of uniaxial anisotropy, is calculated in the context of the mean-field approximation. The tricritical temperature decreases as θ increases, and finally vanishes for θ larger than a certain critical angle. In the (H_∥, H_⊥, T) space there is a line of tricritical points which separates two smoothly joining surfaces of first and of second order phase transitions.