Vector two-point functions in maximally symmetric spaces

We obtain massive and massless vector two-point functions in maximally symmetric spaces (and vacua) of any number of dimensions. These include de Sitter space and anti-de Sitter space, and their Euclidean analogsS ⁿ andH ⁿ. Our method is based on a simple way of constructing every possible maximally symmetric bitensorT _a...bc...d(x, x) which carries tangent-space indicesa...b atx andc...d atx.     

Martensitic transformations in Ti (Ni,Fe) alloys

In this work we used x-ray structural analysis to investigate the martensitic transformations (MTs)B2R andRB19 in Ti(Ni, Fe) alloys containing 1, 2.5, 4, 5 at. % Fe, and the effect of heat treatment on the MT temperatures and sequence. In the majority of cases, it was found that the MTB2R proceeds through a two-phase region (+R). Heat treatment leads to a narrowing of the temperature interval of the existence of the two-phase region, weakly affects the onset temperatures of the MTsB2R T_R andRB19 M_s, and sharply increases the temperature-of the end of the MT M_e. The existence of the two-phase region is related to the two MT channelsB2R andB2B19 initially intrinsic to the allovs of the given compositions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 19–22, December, 1989.     

A new theory on scattering of electrons due to spiral dislocations

The topologically singular lattice structure around a spiral dislocation scatters electrons in a manner much different from the deformation-potential-scattering. Thet-matrix is represented ast(k, k)=t ₀ sin (k _z/2) exp (±i _kk/2)/sin ( _kk/2) with the scattering angle _kk, the componentk _z of the wave vector parallel to the dislocation, andt ₀(Fermi energy). This kind of scattering alone does not cause a perpendicular resistivity, but in a dirty limit a specific dislocation resistivity does exist, whose relaxation time per unit length of dislocation is of the order of/(Fermi energy).Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-KölnOn leave of absence from Department of Materials Science, Hiroshima University, Higashisenda-machi, Hiroshima, Japan     

Sensitivity of approximate formulas for determining optical constants of thin films

The sensitivity of approximate formulas for determining the optical constants of thin films using measurement of reflectancesR and transmittancesT at normal incidence have been investigated theoretically. The ranges of refractive indexn, absorption indexk,2nk (=₂) andn ²–k ²(=₁) within relative errors of 5%, 10%, and 20% may be obtained. Selected signs of (₁)⁺ or (₁)^– have been determined. Validity of the condition n₀ A=n _s A has been also evaluated (A=1–R –T andA=1–R–T).     

Phase transitions on fractal lattices with long-range interactions

A fractal latticeF is defined here to comprise all points of the forma + ma+ m² a+ ... +m^qa^(q), whereq is a nonnegative integer anda, a,..., a^(q)A, whereA is a finite set of points in some Euclidean space. Providedm is not too small (in particular,m must be at least 2), the dimension ofF is shown to beD = log n/logm, wheren is the number of points inA. It is shown further that an Ising model onF, with a ferromagnetic pair interaction r^– between spins separated by a distancer, has a phase transition ifD < < 2D. On the other hand, for > 2D, provided a certain condition which rules out periodic lattices is satisfied, there can be no finite-temperature transition leading to spontaneous magnetization.     

On the equivalence of boundary conditions

We show that ifb andb are two boundary conditions (b.c.) for general spin systems on ^d such that the difference in the energies of a spin configuration in ^d is uniformly bounded, |H _,b ()–H _,b()|C < , then any infinite-volume Gibbs states and obtained with these b.c. have the same measure-zero sets. This implies that the decompositions of and into extremal Gibbs states are equivalent (mutually absolutely continuous). In particular, if is extremal,=. Application of this observation yields in an easy way (among other things) (a) the uniqueness of the Gibbs states for one-dimensional systems with forces that are not too long-range; (b) the fact that various b.c. that are natural candidates for producing non-translation-invariant Gibbs states cannot lead to such an extremal Gibbs state in two dimensions.Supported in part by NSF Grant PHY 78–15920 and by the Swiss National Foundation For Scientific Research.     

Semimodularity and the logic of quantum mechanics

If (, ,P, ) is an event-state-operation structure, then the events form an orthomodular ortholattice (, , ) and the operations, mappings from the set of states into , form a Baer *-semigroup (S, , *, ). Additional axioms are adopted which yield the existence of a homomorphism from (S, , *, ) into the Baer *-semigroup (S(), , *, ) of residuated mappings of (, , ) such thatx S maps states while _x S () maps supports of states. If (, , ) is atomic and there exists a correspondence between atoms and pure states, then the existence of provides the result: (, , ) is semimodular if and only if every operationx S is a pure operation (maps pure states into pure states).Supported in part by the United States Atomic Energy Commission and in part by the Fonds National Suisse.     

Superradiating 4P-4S-3P cascade of sodium vapour arising on the leading edge of the exciting laser pulse

Investigations of the superradiating cascade of sodium vapour 4P-4S-3P ₁ = 2.21 µm and ₂=1.14 µm) arising on the leading edge of the exciting laser pulse were carried out. The dependences of the actual delay time _D of the ₁ pulse on the population rise time of the laser-excited 4P state were measured and compared with those calculated following the existing theoretical model. The dependence of the actual delay time _D on the inverse density of excited atoms 1/N* is also presented. Analysis of this dependence revealed the influence of the Doppler dephasing and of the second, ₂, transition on the formation of the ₁ superradiance.     

A Quantization on Riemann Surfaces with Projective Structure

Let X be a Riemann surface equipped with a projective structure. Let be a square-root of the holomorphic cotangent bundle K _X . Consider the symplectic form on the complement of the zero section of obtained by pulling back the symplectic form on K _X using the map ². We show that this symplectic form admits a natural quantization. This quantization also gives a quantization of the complement of the zero section in K _X equipped with the natural symplectic form.     

Upper bounds for the energy expectation in time-dependent quantum mechanics

We consider quantum systems driven by Hamiltonians of the formH+W(t), where the spectrum ofH consists of an infinite set of bands andW(t) depends arbitrarily on time. Let H (t) denote the expectation value ofH with respect to the evolution at timet of an initial state . We prove upper bounds of the type H (t)=O(t ), >0, under conditions on the strength ofW(t) with respect toH. Neither growth of the gaps between the bands nor smoothness ofW(t) is required. Similar estimates are shown for the expectation value of functions ofH. Sufficient conditions to have uniformly bounded expectation values are made explicit and the consequences on other approaches to quantum stability are discussed.     

Quantum-resolved fluorescence excitation spectra of SnO free radical

TheA ¹ –X ^{1 +} system of SnO is studied by laser- induced fluorescence excitation spectroscopy using isotopically enriched tin Sn¹¹⁶. The rotational structure analysis has been carried out for 6-0, 5-0, 2-0 bands. All these spectra were well resolved only with few perturbed lines in 2-0 band. Rotational constantsB ₂,B ₅,B ₆ and henceB _e , _{e e} have been obtained for the Sn¹¹⁶O molecule. An extension of perturbation study on 4-0 band has been made showing the maximum perturbation occurs at different J values for different isotopes.     

Structural state of Cu-Be-Ag alloys in the process of decomposition of solid solution

Investigation of aging Cu-1.5% Be-2% Ag and Cu-1% Be-4% Ag alloys was carried out in this study by the methods of x-ray analysis of monocrystals, and electron microscopy. In the aging process at 218, 300, and 450C, laminar zones of Guinier-Preston, enriched with beryllium and silver atoms were formed. Entry of silver into the zones widens the upper temperature interval of the zone stage to 450C. With the increase of annealing time the metastable-phase was precipitated. The crystals of -phase are precipitated with orientation in the direction (100) in consequence of interactions of the fields of elastic stresses occurring around -precipitations, and periodic structure is formed in the alloy. The stable phase-CuBe and Ag was precipitated in the Cu-1% Be-4% Ag-alloy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 21–25, August, 1972.     

New interpretation of experiments on the intermediate meson

A new theory of weak interactions is proposed in which the coupling between theV-A currents j(X) and j(X) is achieved not by vector mesons [by a propagator D ^c (X-X)], but by a scalar functionR(X – X), a fermion-antifermion loop which plays the role of a unique film joining two different pointsX andX of completely uncoupled space-times (as a result of which the space becomes a continuum). The existence of the actual currents j results from correlations between the two different spinor layers of Dirac layer formation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 25–40, February, 1996.     

Bounded perturbations of dynamics

If and are one-parameter automorphism groups of a von Neumann algebraM is said to be a bounded perturbation of if _t – _t 0 ast0. We give a complete characterization of the bounded perturbations of . In particular, we show that if can be implemented by a strongly continuous one-parameter group with self-adjoint generator (Hamiltonian)H, then can be implemented in the same way and the corresponding HamiltonianH can be chosen to be of the formH=VHV ^–1+h, whereV is a unitary ofM andh=h*M.On leave of absence from II. Institut für Theoretische Physik, Universität Hamburg, D-2000 Hamburg 50, Federal Republic of Germany     

Phase transformations in Cu-Sn alloys containing Ni,Al, Ge,and In

After quenching from 700C and aging, Cu-Sn alloys containing Ni and Al were found to have a precipitation of-solid solution, with a DO₃ type of ordering, of metastable ,, and phases. It was established that the phase has an 4 type of ordering while the phase has the Cu₃Ti type. Observations revealed that Cu-Sn-Al alloys contained two phases, and, with an identical structure but with different ratios of electron concentration per atom.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 34–37, April, 1981.     

Optimal Gaussian solutions of nonlinear stochastic partial differential equations

We present a linearization procedure of a stochastic partial differential equation for a vector field (X _i (t,x)) (t[0, ),xR ^d ,i=l,...,n): _t X _i (t,x)=b _i (X(t, x)) +D, X _i (t, x) + _i f _i (t, x). Here is the Laplace-Beltrami operator inR ^d , and (f _i (t,x)) is a Gaussian random field with f _i (t,x)f _j (t,x) = _ij (t – t)(x – x). The procedure is a natural extension of the equivalent linearization for stochastic ordinary differential equations. The linearized solution is optimal in the sense that the distance between true and approximate solutions is minimal when it is measured by the Kullback-Leibler entropy. The procedure is applied to the scalar-valued Ginzburg-Landau model in R¹ withb ₁(z) =z - vz ³. Stationary values of mean, variance, and correlation length are calculated. They almost agree with exact ones if 1.24 ( ² ₁ ⁴ /D ₁ ^1/3:= _c . When _c , there appear quasistationary states fluctuating around one of the bottoms of the potentialU(z) = b ₁(z)dz. The second moment at the quasistationary states almost agrees with the exact one. Transient phenomena are also discussed. Half-width at half-maximum of a structure function decays liket ^–1/2 for small t. The diffusion term _x ² X accelerates the relaxation from the neighborhood of an unstable initial stateX(0,x) 0.     

Green Functions of the Stationary Schrödinger Equation and Tomographic Representation of Quantum Mechanics

Invertible maps of operators of quantum observables onto functions of c-number arguments and their associative products are reviewed. In particular, the symplectic tomography map is discussed and an expression connecting an arbitrary operator and its tomographic symbol is written down. This formula is applied to obtain explicit expressions for tomographic symbols, which are symplectic tomograms of Green functions of stationary and nonstationary Schrödinger equations written for the case of harmonic oscillator. The connection between the so-called classical propagator (X,,,t,X,,,0) and the tomographic symbol of the evolution operator of nonstationary Schrödinger equation is found. The spin tomography is presented as a map of operators acting in spinor space onto functions of c-arguments. As an example, the spin located in a magnetic field is considered and the tomographic symbol of resolventa is obtained. Tomographic symbols of hermitian conjugate operators are shown to be complex conjugate functions.     

Relativistic quarks bound with a one-body tensor potential

A dipole fit to electromagnetic form factors is used to determine a quark density in the nucleon. A radial tensor potential is used to bind the quarks into states of goodJ, J _z, and parity. The tensor potential radial component is taken to satisfy the equationT = T ₀, whereT ₀ is a parameter of the model. This linear divergence equation can be simultaneously solved with the Dirac equation for the bound quark wave functions. A self-consistent solution is possible where the mass density used as the source for the binding potential is the same as that determined from the solution for the quark wave functions.     

Stimulated IR- and vacuum-UV emission following two-photon-excitation of molecular hydrogen using an ArF laser

Hydrogen molecules are excited by two 193 nm-photons [X¹ _g ⁺ E,F¹ _g ⁺ ;Q₀₂(1)] generated with a commerical oscillator-amplifier ArF laser. Stimulated emission is subsequently observed in the IR (=752.4 nm to 836.6 nm;E, FB) and in the VUV (=134.0 nm to 160.9 nm;BX) with a VUV conversion efficiency of 0.2%. The rotational fine-structure, the saturation behaviour, pump depletion as well as SRS-onset on and off two-photon resonance are investigated.     

Periodic nonlinear waves on a half-line

Nontrivial solutions of the equationu _tt=u _xx–g(u) which are 2-periodic int and which decay asx are shown to exist ifg(a)=0 andg(0)>1. Breather-like solutions, which also decay asx –, can be interpreted as homoclinic solutions in thex-dynamics; their existence is still in question for generalg.