Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.     

Influence of the vacuum level upon the growth of carbon nanotubes on silicon carbide surface

We have investigated the influence of the vacuum level upon the growth of carbon nanotubes (CNTs) on 6H-SiC () surface.CNTs of about 160 nm in length were formed densely and uniformly on the 6H-SiC surface during annealing at 1700 °C in a high vacuum (∼10⁻² Pa). CNTs of about 1 μm in length were formed during annealing at 1700 °C in an ultra-high vacuum (∼10⁻⁷ Pa). However, CNTs were not formed and SiO₂ layers were formed on the SiC surface at 1700 °C in air. It is found that longer CNTs can grow up in an ultra-high vacuum, moreover, a little aligned and low-density graphite layers, or carbon nanofibers can also grow up.     

Secondary effects on solid surfaces stimulated by the cathode plasma flux in vacuum arcs

The conducting plasma region between the electrodes of a vacuum arc contains single-and multiple-charged ions of the cathode material. Investigation into the behaviour of this flux when it impinges upon a surface should take into account secondary processes. From among various processes on the surface in vacuum arc, particular attention is paid to the sputtering of the surface and to the secondary electron emission by positive ions emitted from the cathode spots. On the basis of the sputtering yield characteristicsS _r as a function of ion kinetic energyE _i and their energy distribution in the cathode flux, the total sputtering yieldsS _re for atomicaly clean surface have been determined. Experimental verification ofS _re was performed by measuring the ratio of mass deposited on the collectors to mass carried by the particle incident flux. It was found that the calculated value ofS _re is comparable to the evaluated one from the experiments. The emission of secondary electrons from clean metal surfaces due to a bombardment by multiple-charged ions is considered. The secondary electron emission _c depends on excess energyE _ex of incident ion and its average value _av for multiple-charged ions depends both on the fractional distribution of ion flux _zi and on the excess energyE _ex of each ion. It is proposed that the relationship derived is applicable to most combinations of atomic ions and pure metal surfaces.Presented at 17^th Symposium Plasma Physics and Technology, Prague, June 13–16, 1995.This work was supported by the State Committee for Scientific Research within the research project No. 3P40101507.     

Depolarization field and properties of thin ferroelectric films with inclusion of the electrode effect

The influence of metallic electrodes on the properties of thin ferroelectric films is considered in the framework of the Ginzburg-Landau phenomenological theory. The contribution of the electrodes with different screening lengths l _s of carriers in the electrode material is included in the free-energy functional. The critical temperature T _cl , the critical thickness of the film, and the critical screening length of the electrode at which the ferroelectric phase transforms into the paraelectric phase are calculated. The Euler-Lagrange equation for the polarization P is solved by the direct variational method. The results demonstrate that the film properties can be calculated by minimizing the free energy, which has a standard form but involves the coefficient of the term P². This coefficient depends not only on the temperature but also on the film thickness, the surface and correlation effects, and the electrode characteristics. The calculations of the polarization, the dielectric susceptibility, the pyroelectric coefficient, and the depolarization field show that the ferroelectric state of the film can be destroyed using electrodes from a material whose screening length exceeds a critical value. This means that the electrodes being in operation can induce a transition from the ferroelectric phase to the paraelectric phase. The quantitative criteria obtained indicate that the phase state and properties of thin ferroelectric films can be controlled by choosing the appropriate electrode material.     

Xanthopoulos Theorem in the Kaluza–Klein Theory

It is shown that if _AB is an exact solution of the Einstein vacuum field equations in 4 + 1 dimensions, R^ _AB = 0, and l _A is a null vector field, then _AB + l _A l _B is also an exact solution of the Einstein equations R^ _AB = 0 if and only if the perturbation l _A l _B satisfies the Einstein equations linearized about _AB. Then, making use of the Kaluza–Klein approach, it is shown that this result allows us to obtain exact solutions of the Einstein–Maxwell equations (possibly coupled to a scalar field) by solving a system of linear equations.     

Hydrogenated amorphous silicon films obtained by a low pressure dc glow discharge

Films of a-Si: H have been deposited by means of a dc hot cathode discharge of SiH₄ with electrostatic confinement at a pressure as low as 0.4 Pa. The plasma used is quite quiescent as has been observed by means of reproducible Langmuir probe measurements. Substrates have been placed at different locations in between the electrodes, some of them facing the anode and the others facing the cathode.Films deposited on substrates facing the cathode present a granular, non-columnar, structure, an IR spectrum with only SiH absorption peaks, and a very low photoresponse. Films deposited on substrates facing the anode have a similar IR spectrum but are homogeneous, have lower hydrogen content, and present a high photoresponse. The optical absorption coefficient shows in all samples thenE=C(E–E₀) ^x behaviour, but with exponentx=3 and notx=2 as is usually considered in a-SiH.     

Influence of radiofrequency power on compositional, structural and optical properties of amorphous silicon carbonitride films

The silicon carbonitride (SiCN) films were deposited on n-type Si (1 0 0) and glass substrates by the radiofrequency (RF) reactive magnetron sputtering of polycrystalline silicon target under mixed reactive gases of acetylene and nitrogen. The films have been characterized by energy dispersive spectrometer (EDS), atomic force microscope (AFM), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and ultraviolet-visible spectrophotometer (UVS). The influence of RF power on the compositional, morphological, structural and optical properties of the SiCN films was investigated. The SiCN films deposited at room temperature are amorphous, and the C, Si and O compositions except N in the films are sensitive to the RF power. The surface roughness and optical band gap decrease as the RF power increases. The main bonds in the SiCN films are C-N, N-H_n, C-H_n, C-C, CN, Si-H and Si-C, and the intensities of the CN, Si-H and C-H_n bonds increase with increment of the RF power. The mechanisms of the influence of RF power on the characteristics of the films are discussed in detail.     

On bianchi type-I vacuum solutions inR+R 2 theories of gravitation. I. The isotropic case

From a LagrangianL= (1/)(-g)^1/2[R/2+l²(R _ik R ^ik+R ²)] one obtains fourth-order field equations for the metrical tensorg _ik. Inserting a 3-flat Robertson-Walker line element, the set of their vacuum solutions will be enumerated completely. The qualitative behavior, and especially the influence of thel ²-terms (which is possibly necessary for the renormalization of quantum gravity) in certain stages of evolution follow from a phase plane analysis. Depending on the sign of coupling, one obtains either exponentially increasing or oscillating solutions at late times as well as special solutions without an initial singularity.     

Properties of the skeleton of aggregates grown on a Cayley tree

We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l ^dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d _l ^s , can be expressed in terms ofd _l asd _l ^s = 1,d _l d _l ^c = 2;d _l ^s = d _l –1,d ₁ d _l ^c = 2, which implies that the tree is finitely ramified ford _l 2 and infinitely ramified whend _l 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.     

Kinetic processes of muonium formation by thermalized electrons in the spur model

Diffusion of a thermalized electron in the field of a Coulomb centre is considered. The time dependence of the probability for the electron not to be captured by the Coulomb centre ( ⁺) at the momentt,P _D (t), is obtained. The quantityP _D (t) coincides with the precession amplitude at the muon frequency and is determined by the parameter/l _CT ( is an averaged distance from an electron to a muon att=0 andl _CT =e ²/(2T) is the Onsager length) that reflects the relation between electron potential and kinetic energies at t=0. When/l _CT –1 the precession amplitudeP _D (t) decreases up to 30% during the timel _CT ² /D-(D-is the diffusion coefficient) and then it becomes almost constant. The dependence ofP _D () on/l _CT is presented.     

Third order nonlinear optical properties of some organic nitroxyls

The degenerate four-wave mixing experiments have been performed in the dichloromethane solutions of 2,2,6,6-tetramethyl-pipridine-4-ol-N-oxyl p-hydroxybenzaldehyde oxime benzoic ester (TPOHBOBE) and bis-(TPOHBOBE) cobalt (II), respectively. The result is in agreement with the theoretical prediction of depending on the molecular chain length l as l ⁵. A large off-resonant third order hyperpolarizability _xxxx of 1.3 × 10^–30 esu for bis-(TPOHBOBE) cobalt (II) was obtained. The corresponding value of the third order nonlinear optical susceptibility ⁽³⁾ _xxxx for its solid state is estimated to be 7.8 × 10^–9 esu.     

Parabolic drift towards homogeneity in large-scale structures of galaxies

To describe the progressive transition in large-scale structures of galaxies from a seemingly fractal behavior at small scales to a homogeneous distribution at large scales, we use a new geometrical framework called entropic-skins geometry which is based on a diffusion equation of scale entropy through scale space. In the case of an equipartition of scale entropy losses in scale space, it is shown that fractal dimension (varying from 0 to 3) depends linearly on the logarithm of scale from the average size l_c of galaxies until a characteristic length scale l₀ beyond which distribution becomes homogeneous. A simple parabolic expression for correlation function can be derived: ln(1+ξ_i)=(β/2)ln²(l_o/l_i) with β=3/ln(l₀/l_c)≈0.32 and . This law has been verified using correlation functions measured on several redshift surveys.     

Influence of multiple elastic scattering on the shape of the elastically scattered electron peak

The influence of multiple elastic scattering on the shape of the energy distribution of elastically scattered electrons is investigated. The energy of the maximum intensity of the detected electrons differs from the probe electron beam energy due to the elastic energy loss. The experimentally observed spectrum is adequately described by a Gaussian distribution with a maximum at the elastic energy loss value. In this paper the peak-broadening mechanisms due to energy-analyzer spread function, probe beam energy distribution and atomic vibration-induced broadening are considered to be independent and of random nature. Analysis of multiple elastic scattering shows some mechanisms leading to the broadening and a shift of the elastic scattering electron energy spectrum from the value defined by single elastic scattering at the certain angle. It is revealed that the magnitude of this shift and the width of energy distribution is determined by ratio (_lin/_ltr)$(l_{\text{in}}/l_{\text{tr}})$, where _lin$l_{\text{in}}$ is inelastic mean free pass, _ltr$l_{\text{tr}}$ is the transport length.     

Vacuum energy and Casimir force in the presence of a dimensional parameter in the boundary condition

The Hamiltonian for a scalar field that satisfies the boundary condition ?? _n ? = (1/δ)? must include a surface potential energy. The corresponding term in the Casimir energy $\tilde E_C$ proves to be a leading one when the dimension of the region is l～δ. The energy $\tilde E_C$ does not involve arbitrariness associated with regularization and is an unambiguously determined function of the field mass m, the size l, and the penetration depth δ. The inclusion of the surface term is of importance for ensuring that the derivative ?? $\tilde E_C$ /?l is equal to the ll component of the vacuum energy-momentum tensor. The Casimir energy $\tilde E_C$ is related to its volume component E _C by a Legendre transformation where the quantity conjugate to 1/δ is the product of the vacuum surface energy and δ. If δ is negative and if ?/mc>|δ|, there exists a critical value l=l _c (δ) above which (l>l _c ) the vacuum is unstable; if a self-interaction of the form ? ⁴ is taken into account, this will lead to a phase transition accompanied by the formation of a condensate of the field ?. If δ=+0 or ∞ and if the dimensionalities are even, it is possible to construct a vacuum energy-momentum tensor (not only energy) that is finite over the entire space. Specially chosen counterterms leave unchanged the analytic dependence of the vacuum energy on the dimensionality of space and the character of the coordinate dependence of the energy density for x>?/mc.     

Kinetic equation in the kinetic region of the dilute and nonuniform electron plasma

Mori's scaling method is used to derive the kinetic equation for a dilute, nonuniform electron plasma in the kinetic region where the space-time cutoff (b, t _c) satisfies _Dbl _f , _D t _{c f} , with _D the Debye length, _D ^–1= _p the plasma frequency, andl _f and _f the mean free path and time, respectively. The kinetic equation takes account of the nonuniformity of the order ofl _f and _D for the single-and the two-particle distribution function, respectively. Thus the Vlasov term associated with the two-particle distribution function is retained. This kinetic equation is deduced from the kinetic equation in the coherent region obtained by Morita, Mori, and Tokuyama, where the space-time cutoff of the coherent region satisfies _Dbr ₀, _Dt _{c 0}, withr ₀ the Landau length and ₀ the corresponding time scale.     

Theoretical analysis of acoustic-optic frequency shifter by dual mode fiber

The frequency shifting between two modes in an optical fiber resulting from acoustic wave propagation has been studied theoretically. Our theoretical results confirm the earlier experimental work. The polarization effect introduced by acoustic waves has been examined as well. The analysis shows that the polarization characteristic and symmetry property of the modes are not preserved in the coupling process of acoustic-optic frequency shifting for arbitrary ratio of the fiber cladding radius to the acoustic wavelengthd/ _a, in contrast to stable mechanical microbending, and that for the givend/ _a = 0.397, the polarized light signal at frequency ₂, shifted from that at frequency ₁, is quasi-linearly polarized for any acoustic-optic interaction length. However, the polarization effect can be neglected when the fiber cladding radius is much smaller than the acoustic wavelength.     

Monte Carlo simulation of many-arm star polymers in two-dimensional good solvents in the bulk and at a surface

A Monte Carlo technique is proposed for the simulation of statistical properties of many-arm star polymers on lattices. In this vectorizing algorithm, the length of each arml is increased by one, step by step, from a starting configuration withl=1 orl=2 which is generated directly. This procedure is carried out for a large sample (e.g., 100,000 configurations). As an application, we have studied self-avoiding stars on the square lattice with arm lengths up tol _max=125 and up tof=20 arms, both in the bulk and in the geometry where the center of the star is adsorbed on a repulsive surface. The total number of configurations, which behaves asNl ^{G–1 fl} , where=2.6386 is the usual effective coordination number for self-avoiding walks on the square lattice, is analyzed, and the resulting exponents G=(f) and _s (f) for the bulk and surface geometries are found to be compatible with predictions of Duplantier and Saleur based on conformai invariance methods. We also obtain distribution functions for the monomer density and the distance of the end of an arm from its center. The results are consistent with a scaling theory developed by us.     

Influence of ambient oxygen pressure on the preferred orientation, microstructures, and dielectric properties of (Ba1-xSrx)TiO3 thin films with compositionally graded structures

Compositionally graded (Ba_1-xSr_x)TiO₃ (BST) thin films, with x decreasing from 0.25 to 0.0, were deposited on Pt(111)/Ti/SiO₂/Si(100) substrates by pulsed-laser ablation at 600 °C and under ambient oxygen pressures ranging from 50 to 400 mTorr. The influence of the ambient gas pressure on the preferred orientation, microstructures, and dielectric properties of compositionally graded BST films was investigated by X-ray diffraction, scanning electron microscopy, and dielectric frequency spectra, respectively. As the ambient oxygen pressure was increased, the preferred orientation evolved in the order: (100)+(110)(110)+(111) random orientation, and the surface roughness of the graded BST films also increased. The graded BST films deposited at high ambient oxygen pressures (300400 mTorr) exhibited a grainy structure with polycrystalline grains throughout the film thickness, whereas the graded films deposited at low ambient oxygen pressures (50200 mTorr) possessed a columnar structure. The evolution of the microstructure was ascribed to the different physical and chemical properties of the species that were incident onto the substrates at the various oxygen pressures. The dielectric properties of the graded BST films were dependent upon the ambient oxygen pressures. The graded BST films deposited at 200 mTorr exhibited the highest dielectric constant. PACS 77.55.+f; 77.22.Ch; 81.15.Fg     

Operator product expansions on the vacuum in conformal quantum field theory in two spacetime dimensions

Let ₁(x) and ₂(y) be two local fields in a conformal quantum field theory (CQFT) in two dimensional spacetime. It is then shown that the vector-valued distribution ₁(x)₂(y)|0 is a boundary value of a vectorvalued holomorphic function which is defined on a large conformally invariant domain. By group theoretical arguments alone it is proved that ₁(x)₂(y)|0 can be expanded into conformal partial waves. These have all the properties of a global version of Wilson's operator product expansions when applied to the vacuum state |0. Finally, the corresponding calculations are carried out more explicitly in the Thirring model. Here, a complete set of local conformally covariant fields is found, which is closed under vacuum expansion of any two it its elements (a vacuum expansion is an operator product expansion applied to the vacuum).Work supported by Deutsche Forschungsgemeinschaft