Nonlocality in (1/N)-expanded nonrenormalizable interactions

Nonrenormalizable interactions are studied on the example of the (1/N) ₆ ⁴ model with interaction via the collective = ² mode. In 4<d<6 dimensions, the model is nonrenormalizable by power counting but it does not require more subtractions than in the four-dimensional case. In six dimensions, nonrenormalizability is essential: There are two induced couplings ³ and . The ³ coupling strength can be determined from the requirement that the effective potential has a minimum at ² = = 0. The nonlocal formafactor produced by an infinite number of insertions cannot be determined uniquely, however the ambiguity concentrates in the leading order only. We construct this formfactor using the method of Efimov and Mogilevsky. The resulting theory satisfies unitarity, microcausality and correct spectral properties.     

H2-induced changes in electrical conductance of β-Ga2O3 thin-film systems

H₂-induced changes of electrical conductivity in polycrystalline, undoped -Ga₂O₃ thin films in the temperature range of 400–650° C are described. The sheet conductance of these films depends reversibly, according to a power law p ^1/3, on the partial pressure of hydrogen in the ambient atmosphere of the Ga₂O₃ film. A bulk vacancy mechanism is excluded by experiments and it is shown that the interaction is based on a surface effect. Changes in conductance are discussed to result from the formation of an accumulation layer due to chemisorption on the grain surfaces. Typical coverages are determined to be approximately 10^–4 ML for pH₂=0.05 bar and T=600° C. A possible explanation of the p ^1/3 power law is provided.     

Quantization of the Maxwell field in linear conformal invariant gauges

It is shown that the generalized Lorentz gauges provide all linear conformal invariant gauges, i.e. gauges such that A =0.     

Kinetics of small perturbations in an isotropic world

Long-wavelength gravitational perturbations are studied in an isotropic expanding universe filled with an ultrarelativistic gas. A kinetic study in the collisionless approximation shows that scalar and vector perturbations which appear at a time ₀ 1/n, where N is the wave vector and is the time coordinate x⁴, grow if the perturbation of the macroscopic momentum density of the gas at time ₀ is nonvanishing. The growth continues until the time ₁=27₀, at which the perturbation of the macroscopic momentum density of the gas vanishes. A solution is also derived for tensor perturbations in the limit n 1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 37–45, April, 1978.     

Unitarizable scalar multipoles

We show that the scalar multipole ( +m ²) ⁿ = 0 forn odd and all massesm0 allows a Gupta-Bleuler-type quantization with a unitary space of physical states.Feodor-Lynen fellow of the Humboldt foundation. On leave from Institut für Theoretische Physik, TU Clausthal, Leibnizstr. 10, D3392 Clausthal-Zellerfeld, W. Germany.     

Lie-symmetry vector fields for linear and nonlinear wave equations

We derive the Lie symmetry vector fields for the linear wave equation u=0 and nonlinear wave equation u=u ³. The conformal vector fields for the underlying metric tensor fieldg are also given. We construct the conservation laws and derive similarity solutions. Furthermore, we perform a Painlevé test for the nonlinear wave equation and discuss whether Lie-Bäcklund vector fields exist.     

Light absorption by free semiconductor carriers in the presence of a laser wave

Within the framework of the conditions ; » ^–1 ( ^–1 is the mean time of momentum relaxation), the coefficient of absorption () of a weak electromagnetic wave by the free carriers of a polar semiconductor is calculated in the presence of a strong wave (of frequency ), for arbitrary values of and . Photon absorption by band electrons is due to these latter interacting with optical phonons (of frequency _o). The problem is solved by using an analogous approach to the theory of the linear Kubo reaction. The results are valid in the absence of electron heating, when a strong wave only influences the scattering probability. The appearance of a photostimulated tail of absorption is predicted for < _o, including the jump () for ( – _o + ) ₀T as well as peaks in the function () at the points _s=s (s=1, 2, 3,...). The value (₁) is determined by the formula for the absorption coefficient for one strong wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 105–109, July, 1981.The authors are grateful to É. M. Épshtein and Sh. M. Kogan for useful discussions.     

On the Surface Pressure for the Edwards-Anderson Model

For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We consider free , periodic and antiperiodic ^* boundary conditions (by symmetry ⁽⁾=^(*)), and prove the bounds We show moreover that at high temperatures ⁽⁾ is close to ^2/4 and ⁽⁾ is close to ^2/4 uniformly in the volume .     

Quantum supports and modal logic

LetA be a quasi-manual with finite operations. Associate to each E = {e ₁ ,..., e_n} A the set _E of modal formulas: (e ₁ ··· e_n), e_i (e ₁ ··· e_i–1 e_i+1 ··· e_n), i=1,..., n. Set _A = {_E|E A}. We show that supports ofA are in one-to-one correspondence with certain Kripke models of _A where the supports are given by {x |A x is true}.On leave from the Department of Mathematics, Pontificia Universidade Catolica, Rio de Janeiro, Brazil.     

Layering transition in SOS model with external magnetic field

For the SOS model defined by the Hamiltonian , where _x , _x ,{1,2,...},h>0,x ^d ,d2 it is shown that in the low-temperature region an infinite sequence of first-order phase transitions takes place whenh»0 and the temperature is fixed.     

Crystallization features of silicon layers on thermo-insulated substrates under nanosecond laser radiation

P-Si layers on c-Si substrate with a thermo-insulating coating (TIC) were irradiated by the 50-ns second harmonic of an Nd-glass laser. Time-resolved measurements, optical microscopy (OM) and scanning electron microscopy (SEM) data for samples with a 0.1–0.9 m p-Si layer and a 0.1 m SiO₂ or 0.16 m Si₃N₄ TIC layer show that if the p-Si layers melt throughout the depth the solidification starts from the surface as well as from the rear. The latent heat released upon coarse grain growth from the rear prevents further crystallization near the top surface and results in partial or complete remelting of the solid phase on the surface.     

Hydroxil and iron ions in YAP: Er laser crystals

⁴S_3/2⁴I_9/2 (1.663m) and⁴I_11/2⁴I_13/2 (2.731m) laser transitions in YAPEr were studied using a material containing Fe, hydroxil impurities and other codopants. Iron impurity causes luminescence quenching of both the⁴S_3/2 and⁴I_11/2 levels whereas OH^– ions enlarge losses, particularly at 2.731m. The effect of iron and hydroxil impurities may be easily diminished by adding Mg²⁺ ions, whereas the admixture of Ce³⁺ or Zr⁴⁺ brings no positive effects.     

Simultaneous detection of atomic and molecular hydrogen using a tunable ArF excimer laser

We report preliminary experiments which demonstrate the simultaneous detection of both atomic and molecular hydrogen using a single tunable ArF laser. The tunable ArF laser was modified to lase simultaneously at two wavelengths by the addition of a second grating to the oscillator stage as in earlier work by Ketterle et al. for KrF operation. To our knowledge, this is the first demonstration of dual-wavelength capability with a tunable ArF excimer. The H atom diagnostic utilized tunable ArF excimer laser output at 193.29 nm which was Raman shifted in D₂ (first Stokes) to generate 205.14 nm radiation which then excited the H atom to its (3s, 3d) states via a two-photon transition. Fluorescence was detected at 656 nm on the (3s, 3d) 2p transition. The second wavelength from the tunable excimer was used to excite several rovibronic LIF transitions of hydrogen molecule via two-photon absorption on the E ¹ _g ⁺ X ¹ _g ⁺ (2,0) band. Fluorescence occurs at 750 nm and 830 nm on the (E ¹ _g ⁺ B ¹ _g ⁺ ) transitions.     

Bianchi and Weyl equations as sufficient equations for Einstein spaces

When the Bianchi equation and the wave equation for the Weyl spinor are written in the form which they take for Einstein spaces, but with the symmetric 4-spinor _ABCD considered arbitrary and with the background space unspecified, ^EA _EBCD=0; (+12) _ABCD –6(AB ^EF ( _CD )EF =0 it is shown that — in general — for this pair of equations to be consistent, the background space has to be an Einstein space, and the symmetric 4-spinor _ABCD has to be the Weyl spinor of this space.     

EPR Spectra of Cr3+ Ions in Sr3Ga2Ge4O14:Cr Single Crystals

The results of investigations of chromiumdoped Sr₃Ga₂Ge₄O₁₄ single crystals by the EPRspectroscopy method are presented. It is shown that activating chromium ions form Cr³⁺ Ga³⁺ (Ge⁴⁺) substitution centers in the 1aoctahedral positions of the lattice of Sr₃Ga₂Ge₄O₁₄. Depending on the combination of occupation of the 3ftetrahedral positions of the first cationic coordination sphere by Ga³⁺ and Ge⁴⁺ ions, Cr³⁺ centers of two types are formed. Their individual magnetic spectra are characterized by axial and rhombic symmetry. The magnetic multiplicity of the axialsymmetry spectrum is equal to unity. There exist rhombicsymmetry centers of two types differing in the orientation of the principal magnetic axes and the value of the spinHamiltonian parameter E. The magnetic multiplicity of the individual magnetic spectra of rhombic centers of each type is equal to three. The detected EPR spectra of Cr³⁺ ions have been described by the spin Hamiltonian of rhombic symmetry. Its parameters and their spread have been determined.     

Correlations between clusterization and electrical properties within fluorite-type anions excess solid solutions: Setting of a model

We proposed a model to correlate, in a continuous manner, the composition dependence of electrical properties and the progressive extension of clusterization when the substitution rate increases in a fluoride anion excess CaF₂-type solid solution of M_1–xM _x ²⁺ F_2+x(=1,2,3). A new classification of clusters is given based on the presence or absence of coexistence between two types of interstitial fluoride ions.The second part of the paper is devoted to the representation of the sum of interstitial fluoride ionsn _{F int} and the sum of vacancies in normal sitesn according to the general equationy=(mx ³+qx)/(x ²+q). This model allows us to correlate the structural and electrical properties of a large number of solid solutions with fluorite-type structure.     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

Gravitation and universal Fermi coupling in general relativity

The generally covariant Lagrangian densityG = + 2K _matter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentialsg _ikand of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form _kl ⁱ = _kl ⁱ for the coefficients _kl ⁱ of the affine connections is postulated a priori. Alternatively, we can interpret the LagrangianG as a functional of , g_ik, and the coefficients _kl ⁱ . Then the _kl ⁱ are determined by the Palatini equations. From these equations and from the symmetry _kl ⁱ = _lk ⁱ for all matter fields with /=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, / becomes dependent on the Dirac current, essentially with a coupling factor Khc. In this case, the Palatini equations define a new transport rule for the spinor fields, according to which a second universal interaction results for the Dirac spinors, besides Einstein's gravitation. The generally covariant Dirac wave equations become the general relativistic nonlinear Heisenberg wave equations, and the second universal interaction is given by a Fermi-like interaction term of the V-A type. The geometrically induced Fermi constant is, however, very small and of the order 10^–81erg cm³     

A New Duality Transformation for Fourth-order Gravity

We prove that for non-linear L = L(R), G = dL/dR 0 the Lagrangians L and ^L(^R) with ^L = 2R/G³ - 3L/G⁴, ^g_ij = G² g_ij and ^R = 3R/G² - 4L/G³ give conformally equivalent fourth-order field equations being dual to each other. The proof represents a new application of the fact that the operator - R/6 is conformally invariant.     

On the correlation for Kac-like models in the convex case

The aim of this paper is to stu the behavior asm tends to of a family of measures exp[- ^(m)(x)]dx ^(m) on ^m , where ^(m) is a potential on ^m which is a perturbation in a suitable sense of the harmonic potential _j x _j ² .