The Split of the Dirac Hamiltonian into Precisely Predictable Energy Components

We are dealing with the Dirac Hamiltonian H = H₀ + V with no magnetic field and radially symmetric electrostatic potential V = V(r), preferably the Coulomb potential. While the observable H is precisely predictable, its components H₀ (relativistic mass) and V (potential energy) are not. However they both possess precisely predictable approximations H₀ and V which approximate accurately if the particle is not near its nucleus. On the other hand, near 0, H₀ and V are practically unpredictable, perhaps in agreement with the fact, that a neutrino also should be in the game. [We have not yet studied the corresponding observables for the ( 12-dimensional) problem of electro-weak interaction.] Mathematically we are focusing on the spectral theory of the unbounded self-adjoint operators H₀ and V . We can prove that V is unitarily equivalent to V(r) again, by a unitary map given as Wiener-Hopf-type singular integral operator in the standard separation of variables for radially symmetric Dirac Hamiltonians. [This is, as far as the continuous spectrum is concerned.] Very similar unitary equivalence holds for H ₀ and H ₀. We are tempted to regard this as a form of renormalization.     

The critical point indices of ferroelectric and ferromagnetic phase transitions

Magnetic transitions are described by the critical indices0,1/3,4/3 while some ferroelectric transitions appear to give0,R~1/2,1. It is pointed out that these two sets of values for the critical indices are allowed by the scaling laws and stability conditions near the phase transitions.The authors thank Prof. R. S. Krishnan for his encouragement and Mr. B. Viswanathan for some discussions. The financial assistance from DAE and CSIR is also acknowledged.     

On the homotopical significance of the type of von Neumann algebra factors

The set of all projections and the set of all unitaries in a von Neumann algebra factorA are studied from the homotopical point of view relative to the operator norm topology.Two projectionsE andF can be deformed continuously to each other if and only ifEF and 1–E1–F where denotes the equivalence of projections inA in the sense of von Neumann. In other words, the relative dimension and co-dimension are a complete homotopical invariants of projections inA and label pathwise connected components of the set of projections.The first homotopy group ₁(U(A)) of unitaries inA is shown to be 0 forA of infinite type. For typeII ₁ and typeI _n factors, ₁(U(A)) are isomorphic to additive groups of realsR and integersZ, respectively, in which the first homotopy group ₁(F U(A)) of the center ofU(A) is imbedded asZ andnZ, respectively.     

Theory of percolation in fluids of long molecules

We use the reference interaction site model (RISM) integral equation theory to study the percolation behavior of fluids composed of long molecules. We examine the roles of hard core size and of length-to-width ratio on the percolation threshold. The critical density _c is a nonmonotonic function of these parameters exhibiting competition of different effects. Comparisons with Monte Carlo calculations of others are reasonably good. For critical exponents, the theory yields =2=2 for molecules of any noninfinite lengthL. WhenL is very large, the theory yields _cL ^–2. These predictions compare favorably with observations of the conductivity for random assemblies of conductive fibers. The threshold region where asymptotic scaling holds requires the correlation length (/ _c ) ^–v to be much larger thanL. Evidently, the range of densities in this region diminishes asL increases, requiring that density deviations from _c be no larger thanL ^–2. Otherwise, crossover behavior will be observed.     

Observed difference between the probabilities of recoilless resonance absorptionf′ and reemissionf″ of gamma-quanta in single crystals of Na2[Fe(CN)5NO]·2 H2O

The recoilless absorption probability factor,f, and recoilless reemission,f, both measured on Na₂[Fe(CN)₅NO]·2 H₂O single crystals using the black filter technique, were found to be different. Unexpectedly, the results found weref>f. In the calculation off, selfabsorption in the scatterer, non-ideality of the black filter and the influence of non-resonant scattering processes have all been taken into account. By varying the scattering geometry for the incoming and outgoing -beam relative to the crystallographic axes only a change in the reemitted valuesf _a, f_b, f_c could be detected because of the long lifetime of the excited nucleus (10^–7 s) relative to the lattice vibration frequencies (10¹² Hz).     

The Yang-Lee edge singularity in spherical models

The density of Yang-Lee zeros in the thermodynamic limit is discussed for ferromagnetic spherical models of general dimensionalities and arbitrary range of interaction. In all cases the zeros lie on the imaginary axis in the complex magnetic field planeH=H+iH with a density (H) that exhibits a square root singularity(H) (H-H ₀), with=1/2, as the edge of the gap atH=H ₀(T) is approached forT>T _c. WhenTT _c one hasH ₀(T)(TT _c ) with critical exponent=+.Supported by the National Science Foundation in part through the Materials Science Center at Cornell University.     

Local magnetic moment and hyperfine field in hydrogenated iron and iron-vanadium alloy

The local magnetic moment and hyperfine fieldB _hf at Fe and V sites in hydrogenated iron and iron-vanadium were calculated using the discrete variational method. The variations in andB _hf with H occupation of the octahedral (O) site were considered. It was found that when H occupies the O site neighbouring an Fe atom, both local moment and hyperfine field at this atom decrease linearly with increasing number of H atoms. The rate of decrease is larger for Fe in iron as compared to iron in vanadium. On the other hand, when H resides at an O site next neighbouring an Fe atom, whether in iron metal or in iron-vanadium, the Fe magnetic moment increases slowly, while the hyperfine field remains almost constant. The V moment in iron, which is negative (–0.83 _B ), becomes less negative (–0.30 _B) as H occupies the neighboring O sites, whereas slight changes occur (–0.88 _B) when H is at the next neighbouring O site. The net effect of H on Fe in iron is to decrease the average magnetic moment at a rate of 1.2 _B per H/Fe for low H content. On the other hand, the average Fe moment in an iron-vanadium alloy increases if H resides at O sites which are immediate neigbours of V and next neighbours of Fe. This may explain the development of a magnetic state on hydrogenation of Fe-V alloys, which is exhibited by the specific heat and susceptibility measurements. The changes in the isomer shift were found to agree with experimental trends.     

Radiometric observations of the 752.033-GHz rotational absorption line of H2O from a laboratory jet

The intensity and lineshape of the Doppler-broadened 752.033-GHz (2₁₁ 2₀₂) rotational transition of H₂O has been studied passively using a high-resolution two-stage heterodyne radiometer with single-sideband system noise temperature of 45,000 K. The purpose of the experiments was to demonstrate the observability at submillimeter wavelengths of a high-altitude rocket plume simulated by a laboratory H₂O jet in a vacuum chamber. First-stage mixing was accomplished by means of a GaAs Schottky diode with first local-oscillator power supplied by a CO₂-laser pumped formic-acid laser (761.61 GHz), generating and X-band IF signal. Second localoscillator power was provided by a tunable C-band source. One-MHz resolution capability was obtained by means of a 3-GHz waveguide cavity filter with only 9-dB insertion loss. In the H₂O jet experiments, the center frequency of the line was determined to within 1 MHz of the previously reported value. A rotational temperature 75 K, a linewidth 5 MHz, and a Doppler shift 3 MHz (from a 45-degree rotation of the flow direction) were measured with the line-of-sight intersecting the jet axis at a distance downstream of 30 nozzle diameters. These absorption data were ogtained against continuum background radiation sources at temperatures of 1175 and 300 K.     

Electric quadrupole interaction at181Ta in RNi5 compounds

The time differential perturbed angular correlation measurements in PrNi₅, NdNi₅, GdNi₅, DyNi₅ and ErNi₅ rare-earth intermetallics with¹⁸¹Ta as probe nuclei have revealed that these impurity nuclei experience a non-axial electric quadrupole interaction. In all the cases, except in GdNi₅, the interaction frequency has a single value in the range 15–20 MHz with asymmetry parameter 0.98. In GdNi₅, however, there are two interaction frequencies (13.61 MHz and 26.89 MHz), the former being the dominant one (90%) with 0.35 and the latter (10%) with 0.98. It is concluded that in all cases the probe nuclei experiencing the highly asymmetric electric field gradient (efg) occupy the unique Ni(3g) site. Annealing studies have shown that in the case of GdNi₅ the interaction gets highly damped, while there is negligible effect in the other cases. The temperature variation of the efg in all cases seems to follow the empiricalT ^3/2 relation.     

A characterization of Robertson-Walker spaces by null sectional curvature

ForN a null vector andA a vector perpendicular toN, define the null sectional curvature, with respect to TV, of the planeN A ask _N(N A) = R(N,A)A,N<A,A.Then Robertson-Walker metrics can be locally characterized as those for whichk _n at each point is a constant for all the null plans at that point (in each null direction,N must be appropriately chosen). A global characterization of Robertson-Walker spaces is achieved by adding completeness and causality hypotheses.     

The creation of Au nanoscale surface patterns by the low energy Ar + beam irradiation of Au clusters evaporated onto a SiO2/Si surface

Ex-situ contact-mode atomic force microscopy (C-AFM) was used to study the evolution of the topography of nanoscale Au clusters, deposited onto SiO₂/Si surfaces, as a function of Ar⁺ beam irradiation. Various nanoscale Au surface patterns were created, at an ion beam energy of 2.5 keV, by controlling the ion beam conditions. These patterns include ordered or disordered spheres as well as a nanoporous metal layer. We found that the original ( 4 nm) clusters coalesced, under the ion beam, to form both larger clusters ( 9 nm) and a nanoporous interphase layer ( 6.5 nm). Under continued irradiation, both the original clusters and the nanoporous layer were absorbed into the larger clusters.PACS 39.29+k; 81.16.-c; 61.46.+w     

Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

Duality-invariant orthogonality relation between the magnetic monopole and associated quark charges

Duality invariance of the Dirac-Schwinger charge-symmetric theory for electromagnetism leads one to consider the complex-valued amplitudes ₁ and ₂ for the separation between the magnetic monopole and quarks in the logarithmic charge plane. It is observed that the orthogonality relation on the latter amplitudes, Re( ₁ ^* ₂)=0, is equivalent to the equation (ln 9 ^–1)(ln 2)=(1/2) ², which is indeed satisfied by the experimental value fora to within 0.027%. In addition to fixing the unit of electric charge at a primary physical value, the orientation of ₁, ₂ may also prescribe the Cabibbo angle to have the theoretical value 12.4438.     

Isotope effects in the interaction of hydrogen and deuterium with a rhodium (110) surface

The adsorption of H₂ and D₂ on a Rh (110) surface at 100 K leads to a sequence of ordered phases, among others 1×2 phases at _H =0.5 and at _H =1.5 which likely involve a partial surface reconstruction consisting of a small perpendicular displacement of Rh surface atoms. The structure of the adsorbate phases is strongly correlated with the binding energy of the adsorbed phases. Three H (D) binding states (₁,₂ and) are populated at saturation as determined by thermal desorption spectroscopy (TDS). Whereas the peak temperature of the state is invariant with the hydrogen isotope, the D ₁ state appears at a 8 Klower and theD ₂ state at a 5 Khigher temperature than the respective H states. Generally the D phases exhibit a better long-range order than the H phases. The rate of adsorption is identical for the first three adsorbed phases but D₂ adsorbs appreciably faster in the 1×2–3H and the final l×1–2H phases.Zero point energy effects as well as a H coverage dependent local interaction model could account for the observed effects.     

Spin fluctuations in both the ordered and paramagnetic phases of MnSi! MnSi a heavy Fermi liquid?

Polarised neutrons and polarisation analysis have been used to determine the diffuse magnetic scattering from MnSi as a function of temperature. Measurements at 50 K (1.72T _c) and 100 K (3.45T _c) in the paramagnetic phase confirmed the presence of strong spatial correlations previously reported at 300 K (10T _c) and 580 K (20T _c). The spatial correlations between regions of spin density separated by 12 Å are of a ferromagnetic nature and determine the static susceptibility. Integration of the paramagnetic response over an inverse atomic volume yields a moment per manganese atom of 1.2 _B , a value considerably larger than the 0.4 _B observed in Bragg scattering and magnetisation measurements at 4.2 K. Measurements made at 11 K in the ordered magnetic phase reveal strong diffuse scattering corresponding to 0.8 _B per Mn atom. The increase in the diffuse scattering observed in the paramagnetic phase corresponds to the passage of the Bragg component into the background.The presence of significant scattering in the ordered phase and the very unusual wave vector dependence of the diffuse scattering observed at 11 K has been interpreted assuming MnSi to be a heavy Fermi liquid. Furthermore we believe these measurements give the first direct observation of the exchange hole.     

Onset of superconductivity at 107K in YBa2Cu3O7 − δ at high pressure

Electrical resistivity measurements under pressure have been carried out on the high-temperature superconductor YBa₂Cu₃O_{7 –} as a function of temperature T between 1 and 300 K at various pressures between 8 kbar and 149 kbar. The superconducting transition temperature T_c increases almost linearly with pressure at the rate dT_c/dP - 0.13 K/kbar. The onset of T_c, defined as the temperature at which(T) drops to 90% of its extrapolated normal state value, increases from 95 K at 8 kbar to 107 K at 149 kbar. These results suggest that higher pressures will yield yet higher values of T_c.     

Cubic nonlinear tensor of a ferromagnet

The nonlinear properties of a ferromagnet are studied. Many-time retarded Green's functions are used to obtain an expression for the cubic nonlinearity tensor with allowance for spatial dispersion of a uniaxial ferromagnet. The components due to the dipole-dipole interaction of the spins and also due to the anisotropy energy are found. A comparative analysis is made of the different components of the cubic nonlinearity tensor in both the nonresonance case and for various resonances, in particular when ₀, 3 2w₀, 2 ₀, 3 ₀ for the case in tripling of the frequency. Here, is the frequency of the incident wave and ₀ is the frequency of uniform precession. It is shown that in the non-resonance case the largest components are those that are nonvanishing when no allowance is made for spatial dispersion; in the resonance cases the largest components are those due to the dipole-dipole interaction of the ferromagnetism spins.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 53–58, December, 1973.     

Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

The transition from the ordered commensurate phase to the incommensurate Gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields (h, v). In the (h, v) plane, the phase boundary is approached along straight lines v = k h, where (h, v) measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski–Talapov transition f const(h)^3/2 for any direction other than the tangential one. In the latter case f shows a discontinuity in the third derivative.     

μSR studies in an I2-doped phenylenediamine polymer

We report SR studies of the recently synthesized I₂-doped phenylenediamine polymer. Longitudinal-field spectra exhibit typical behavior of a spin-glass with a freezing temperatureT _g 100 K and a spontaneous static local field 500 G at low temperatures. Preliminary magnetization measurements hint of antiferromagnetic spin coupling and hysteretic behavior aroundT _g. These features suggest possible spin-glass and/or antiferromagnetic spin freezing with a high transition temperature due to the doped radical spins in this organic polymer.Postdoctoral fellow of the Humboldt Foundation.     

Decay of the Two-Point Function in One-Dimensional O(N) Spin Models with Long-Range Interactions

Using Griffiths and Lieb–Simon type inequalities, it is shown that the two-point function of ferromagnetic spin models with N components in one dimension decays like the interaction J(n)n ^– provided that 1N4 and T>T _c.