A remark on extensions of quasi-free derivations on the CAR-algebra

Let δ be a quasi-free derivation of the CAR algebra, and let be a closed *-derivation which is an extension of δ. We use Price's techniques from [6] to show that if the polynomials in the linear field operators a(f)→a ^* (f) in D( ) is a core for , then is quasi-free.     

Antihydrogen synthesis: A progress report

The main suggested routes for atomic antihydrogen ( ) formation will be reviewed in a pedestrian fashion. These are the following reactions: , and (iii) . The present status of the projects related to these reactions, as well as the projects' experimental scope, will also be discussed or referred to. Some speculations will be made regarding the physics that can be yielded by an antihydrogen probe.     

Parity anomaly in a \mathcal{P}\mathcal{T}-symmetric quartic Hamiltonian

In this paper, two independent methods are used to show that the non-Hermitian -symmetric wrong-sign quartic Hamiltonian H = (1/2m)p ² − gx ⁴ is exactly equivalent to the conventional Hermitian Hamiltonian . First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated by using functional-integration methods. As the linear term in the Hermitian Hamiltonian is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly is a consequence of the broken parity symmetry of the original non-Hermitian -symmetric Hamiltonian. The anomaly term in remains unchanged if an x ² term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states.     

Antihydrogen at sub-Kelvin temperatures

We discuss the behavior of magnetically trapped antihydrogen ( ) at temperatures relevant for gravity and spectroscopy experiments (well below 1 K) and the possibilities of attaining these temperatures. Two possible options are considered. In the discussion of the first one, i.e. as admixture in cold H gas, we develop the quantum-mechanical theory of -H (and also -H) elastic and rearrangement collisions at ultra-low (sub-Kelvin) energies, when s-wave scattering in the incoming channel dominates. The rate constant of rearrangement leading to decay turns out to be large, which makes the possibilities for collisional cooling in H gas and -H coexistence rather limited. As we show, the most promising is the other option, i.e. atoms in the collisionless regime. For this regime the possibility of one-dimensional adiabatic cooling of is demonstrated by using the example of the Ioffe trap. This phenomenon, interesting from the fundamental point of view, offers the opportunity to cool below 1 mK.     

Amplitude-squared squeezing in superposed coherent states

We study amplitude-squared squeezing of the Hermitian operator Z_θ=Z₁ cosθ+Z₂ sin θ, in the most general superposition state , of two coherent states and . Here operators Z_1,2 are defined by , a is annihilation operator, θ is angle, and complex numbers C_1,2 , α, β are arbitrary and only restriction on these is the normalization condition of the state . We define the condition for a state to be amplitude-squared squeezed for the operator Z_θ if squeezing parameter , where N=a⁺a and . We find maximum amplitude-squared squeezing of Z_θ in the superposed coherent state with minimum value 0.3268 of the parameter S for an infinite combinations with α- β= 2.16 exp [±i(π/4) + iθ/2], and with arbitrary values of (α+β) and θ. For this minimum value of squeezing parameter S, the expectation value of photon number can vary from the minimum value 1.0481 to infinity. Variations of the parameter S with different variables at maximum amplitude-squared squeezing are also discussed.     

Present and future experiments in nonequilibrium reactor antineutrino energy spectrum

Considerable efforts that have been undertaken in recent years in low-energy antineutrino experiments require further systematic investigations in line of reactor antineutrino spectroscopy as a metrological basis of these experiments. We consider some effects associated with the nonequilibrium of reactor radiation and residual emission from spent reactor fuel in contemporary experiments. The text was submitted by the authors in English.     

Grain growth in ice

Summary Grain growth is studied in polycrystalline ice, consisting of elongated grains, of (200÷300) μm mean width and (2÷3) mm mean length . The samples are annealed at different temperatures, between 0°C and −10°C. It is found that is not affected by annealing, while increases with the annealing time. Below the melting point, (t) tends to a limit value . This behaviour is related to the pinning action of air bubbles, which would be similar to that found for solid inclusions in metals. By assuming where is the mean bubble diameter andf is the volume fraction of air dissolved in water, reasonable values are found for . The activation energy of the phenomenon is evaluated on the basis of the present and of Jellinek and Gouda's results. It is foundQ=0.6 eV, which value approximately coincides with that for bulk self-diffusion as it occurs for metals, several degrees below the melting point. This coincidence suggests that, for ice, grain growth would be controlled by bulk impurity diffusion up to the very melting point. Instituto de Matemática, Astronomía y Física, Universidad Nacional de Córdoba and CONICET.     

Comment on “Evaluation of concentration-depth profiles by sputtering in SIMS and AES” by S. Hofmann

The statistics of the sputtering process, which has been used to explain sputterbroadening effect due to surface roughness, has been treated with conditional probabilities. This results in the relationship, , instead of derived by S. Hofmann [Appl. Phys.9, 59 (1976)], where δz,z, and are the depth resolution, sputtered depth and sputtering yield, respectively.     

Image states on beryllium surfaces with low indices

Using the self-consistent pseudopotential method, we have calculated the binding energy of the image states for the (0001) , and surfaces of beryllium. It is shown for the (0001) face that there exists a pronounced resonance image state with n=1 and energy −0.95 eV at the point of the surface Brillouin zone. In the surface, which has a wide band gap in the vicinity of the vacuum level, the calculated image state with n=1 at the point has energy −1.2 eV and is a surface state of gap type. For the face in the vicinity of the point band gaps are absent. However, the symmetry of the bulk states near the vacuum level enables the existence of a resonance image state with n=1 and energy −0.6 eV. Fiz. Tverd. Tela (St. Petersburg) 41, 935–940 (June 1999)     

Algebraically special left-flat spaces and their associated space-times

In a recent paper it was shown how to construct, under certain circumstances, asymptotic (Newman-Unti) series expansions for the spin-coefficient variables for real space-times from data obtained from a given left-flat space in an appropriate frame. If these expansions represent asymptotically flat space-times the latter have the given left-flat space as their H space. The method was described in a frame in which the asymptotic left-shear was zero whereas was not. For the discussion of algebraically special left-flat spaces it is more convenient to have vanish and remain nonzero. In this paper we determine all algebraically special left-flat spaces with diverging rays, utilizing Penrose's conformal technique, and then show in detail how to find the “initial data” for the construction of asymptotic series expansions for the corresponding real space-times.     

Inhomogeneous contact processes on trees

We consider an inhomogeneous contact process on a tree of degreek, where the infection rate at any site isλ, the death rate at any site in isδ (with 0 <δ ⩽ 1) and that at any site in is 1. Denote by the critical value for thehomogeneous model (i.e.,δ=1) on and byϑ(δ, λ) the survival probability of the inhomogeneous model on . We prove that whenk > 4, if , a subtree embedded in , with 1 ⩽σ ⩽ √k, then three existsδ _c ^σ strictly between ( ) and 1 such that ( ) whenδ >δ _c ^σ andϑ(δ, λ _c( ) > 0 whenδ <δ _c ^σ ; ifS={o}, the origin of , then for anyδ ε (0, 1).     

A study of the nuclear-medium influence on neutral-strange-particle production in deep-inelastic neutrino scattering

The influence of nuclear effects on the production of neutral strange particles (V ⁰) is investigated using the data obtained with SKAT propane-freon bubble chamber irradiated in the neutrino beam (with E _v =3−30 GeV) at the Serpukhov accelerator. The mean multiplicity of V ⁰ particles in nuclear interactions, , is found to exceed significantly that in “quasideuteron” interactions, . The ratio of is larger than that for π⁻ mesons, . It is shown that the multiplicity gain of V ⁰ particles can be explained by intranuclear interactions of produced pions. The text was submitted by the authors in English.     

Superconducting states of the cylinder with a single vortex in magnetic field according to the Ginzburg-Landau theory

Self-consistent solutions of the nonlinear Ginzburg-Landau (GL) equations are investigated numerically for a superconducting (SC) cylinder, placed in an axial magnetic field, with a single vortex on the axis (m=1). Two modes, which show the original state of the cylinder, SC or normal (s ₀ andn ₀), are studied. The field increase (FI) and the field decrease (FD) regimes are studied. The critical fields destroying the SC state withm=1 are found in both regimes. It is shown that in a cylinder of radiusR and GL-parameter ϰ, there exist a number of solutions depending only on the radial co-ordinater corresponding to different states such as M,e, d, p,i, n, ,n ^*, and the state diagram on the plane of the variables (ϰ,R) is described. The critical fields corresponding to intrastate transitions and the onset of hysteresis are obtained. The critical fieldH ₀(R) dividing the paramagnetic and diamagnetic states of the cylinder withm=1 is determined. The limiting fields of supercooling or superheating of the normal state at which the restoration of the SC state occurs are established. It is shown, that (in both casesm=1,0) there exist two critical parameters, and , which divide bulk SC into three groups (with and ), in accordance with the behavior in a magnetic field. The parameters and mark the boundary for the existence of a supercooled normal -state in FD-regime and a superheated SC M-state in FI-regime respectively. It is shown, that the value , which was claimed in a number of papers as related to type-I superconductors, is illusory. We regret to inform that Professor Gely Zharkov passed away on 9th July 2004.     

NMR dynamics in disordered magnets

The excitation dynamics of site diluted magnets can be described at low energies (long length scales) by magnons, and above a crossover frequency, ω_c, (short length scales) by fractons. The density of fracton states is given by , where is the fracton dimensionality. Dilution gives rise to a characteristic length ξ∝(p−p _c)^ν, wherep _c is the critical concentration for (magnetic) percolation. The crossover frequency ω_c is proportional to ξ^-1[1+(θ/2)], where θ is the rate at which the diffusion constant decays with distance for diffusion on an equivalent network. A fractal dimensionD describes the density of magnetic sites on the infinite network, and . For percolating networks, for all dimensions ≥2. Neutron scattering structure factor measurements by Uemura and Birgeneau compare well with calculations using fracton concepts. Magnons are extended at low energies, while the fracton states are geometrically localized, with a wave function envelope proportional to exp . Here, is the fracton length scale at frequency ω. The exponentd _ϕ lies between 1 andd _min, the chemical length index (of the order of 1.6 in three dimensions). The localization of the magnetic excitations causes a spread in the NMR relaxation rates. A given nuclear moment will experience only a limited set of fracton excitations, resulting in an overall non-exponential decay of the NMR relaxation signal. When strong cross-relaxation is present, the relaxation will be exponential, but the temperature dependence will be strongly altered from the concentrated result.     

Electric field strength at and near the cathode edge in a magnetically insulated coaxial diode

For an annular cathode in a coaxial diode it has been shown that the averaged electric field strength at the end face of the cathode, E_n, depends on the edge thickness h as

Effect of a magnetic field on the yield point of NaCl crystals

A constant magnetic field is found to have a substantial effect on the macroplasticity of NaCl crystals when they are being actively strained at a constant rate during magnetic treatment. We have measured the dependence of the yield point σ _y on the magnetic induction B=0–0.48 T and the strain rate . It is shown that this magnetic effect has a threshold character and is observed only for B>B _c , where B _c grows with increasing as . The lower the strain rate , the larger the relative decrease in the yield point σ _y (B)/σ _y (0) at fixed field B>B _c . At small enough strain rates the threshold field B _c ceases to depend on and goes constant. A theoretical model is proposed which is in good agreement with the observed regularities. The model is based on the competition between thermally activated and magnetically stimulated depinning of dislocations from paramagnetic impurity centers. Zh. éksp. Teor. Fiz. 115, 951–958 (March 1999)     

Orientational order of uniaxial nematic liquid crystals using electron spin resonance of solute molecules

Summary We present here measurements of hyperfine splittings andg factors of two nitroxide spin probes dissolved inp-azoxyanisole, a wellknown uniaxial nematic liquid crystal, about one part to a million in their molecular ratio. The spin probe molecules used are 1) 17β-hydroxy-4′, 4′-dimethylspiro-/5α-androstane-3, 2′-oxazolidin/-3′-yloxyl, and 2) 2-(3-Carboxypropyl)-4, 4-dimethyl-2-tridecyl-3-oxazolidinyloxyl methyl ester; the former is known to have rigid and the latter flexible structures. These results are used to demonstrate the validity of our model that relates the orientational-order tensor of liquid crystals to the above quantities obtained by the electron spin resonance technique. The model is free of restrictions on the nature of the solute molecules, rigid or flexible. The relation between these directly measured quantities and the components of is established in two steps: first by relating them to , an order parameter tensor defined by a unit vector along the so-called long axis of solute molecules, and then by the use of , wherek is a scalar constant. This latter relation is obtained on the plausible arguments of solute-solvent and solvent-solvent interactions giving rise to and , respectively, andk representing their relative strengths. In spite of appreciable structural differences existing between these two solute molecules, very satisfactory agreements between the theory and experiment are observed for both. Such agreements are essentially independent of uncertainties in our knowledge of the parameters involved. Furthermore, we show that important molecular parameters can also be obtained from such measurements. Deceased.     

Self-assembled fluids with order-parameter-dependent mobility: The large-N limit

The effect of the order-parameter-dependent mobility, , on phase-ordering dynamics of self-assembled fluids is studied analytically within the large-N limit. The study is for quenching from an uncorrelated high temperature state into the Lifshitz line within the microemulsion phase. In the later stage of the ordering process, the structure factor exhibits multiscaling behavior with characteristic length scale The order-parameter-dependent mobility is found to slow down the rate of coarsening.