Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

Reflection electron energy-loss spectra of the fullerenes C60 and C70

High purity polycrystalline samples of C₆₀ and C₇₀ were obtained and studied by the electron energy-loss spectroscopy in the reflection mode. The spectra were used for determination of the loss functions of fullerenes. Loss functions of the fullerenes were compared with those of graphite. It was established that the relative intensities of the peaks corresponding to (+)- and -plasmons depended on the primary electron energy, while the (+)-plasmon energies did not depend on the primary electron energy and were equal to 25.0 eV for C₆₀ and 24.8 eV for C₇₀. The conclusion on the space localization for plasma occilations in fullerenes was made on the base of the study of the energy dependent loss functions.     

Nonperturbative corrections to the cross section ratio R=σL/σT for deep-inelastic scattering

The contribution of nonperturbative corrections, proportional to the quark and gluon vacuum condensates, to the ratio R=_L/_T, where _L and _T are the cross sections for longitudinal and transversal photon scattering by nucleons, is calculated. It is shown that these condensate corrections amount to 30% in the range 0.1相似文献   

Generalization of the relativistic string model in the geometrical approach

We present a model of a one-dimensional extended relativistic object, whose motion is defined by the requirement that its time track in Minkowski space is a surface of the constant mean curvature H. The world surface of the relativistic string is a particular case of such surfaces, namely, a minimal surface with H=0. By differential-geometry methods the theory of the proposed object moving in three-dimensional space-time is reduced to one nonlinear equation – = Hsh. In the theory under consideration, there naturally arises the pair of Lax's operators needed to solve this nonlinear equation by the inverse scattering method.     

Electronic and rotational excitation of H2 by positron impact

The body frame fixed nuclei and the laboratory frame rotational close coupling approximations have been employed to calculate electronic excitation of H₂ (X¹ _g ⁺ B¹ _u ⁺ ) by positron impact. Two electronic states (X¹ _g ⁺ and B¹ _u ⁺ ) and three rotational states in both the elastic and excitation channels are retained in the calculations. Results are reported for electronically elastic, excitation and rotational cross sections up to the incident energy 75.0 eV. The elastic cross sections are found to be influenced significantly with the addition of B¹ _u ⁺ state in the expansion scheme, in both the models used. Above the incident energy of 25.0 eV, the electronic excitation cross sections using the laboratory frame differ significantly from those of the fixed nuclei model.     

The Static Cylinder, Gyroscopes and the C-Metric

The physical meaning of the Levi-Civita spacetime, for some "critical" values of the parameter , is discussed in the light of gedanken experiments performed with gyroscopes circumscribing the axis of symmetry. The fact that = 1/2 corresponds to flat space described from the point of view of an accelerated frame of reference, led us to incorporate the C-metric into discussion. The interpretation of as an angle coordinate for any value of , appears to be the origin of difficulties.     

Photoabsorption of BCl3 Gas under pulsed ArF excimer laser irradiation

The gas immersion laser doping (GILD) technique requires the measurement of the fraction of incident light absorbed in the gas phase during the irradiation with a pulsed laser. Here we report the absorption of boron trichloride (BCl₃) gas at the wavelength of a pulsed ArF excimer laser (=193 nm). We have determined the one-photon (₁) and two-photon () absorption cross sections of this dopant gas for 193 nm. The values of ₁ and are 3.6×10^–20 cm² and 9×10^–45 cm⁴·s, respectively. However, the distinction between simultaneous and sequential absorption has not been possible. Based on these results, we have established a relationship which allows the calculation of the fraction of incident light absorbed as a function of incident intensity and gas pressure.     

Multicomponent composites,electrical networks and new types of continued fraction II

The outstanding problem of systematically developing rigorous bounds on the complex effective conductivity tensor * ofd-dimensional,n-component composites withn>2 is solved. The bounds incorporate information contained in successively higher order correlation functions which reflect the composite geometry. Explicit expressions are given for many of the bounds and some, but not all of them, are represented by nested sequences of circles in the complex plane that enclose, and in fact converge to, each diagonal element of *. They are derived from the fractional linear matrix transformations found in Part I that recursively link * with a hierarchy of complex effective tensors ^(j),j=0, 1, 2, ..., of increasing dimension,d(n–1) ^j . Elementary bounds on ^(j) confining the diagonal elements of ^(j) or its inverse to half-plane, wedge or open polygon regions of the complex plane, imply narrow bounds on * which converge to the exact value of * in the limit asj . When the component conductivities are real these bounds are more restrictive than the corresponding variational bounds. Besides applying to the effective conductivity *, the bounds extend to a wide class of matrix-valued multivariate functions called -functions, and thereby to conduction in polycrystalline media, viscoelasticity in composites, and conduction in multi-component, multiterminal, linear electrical networks. The analytic and invariance properties of -functions are explored and within this class of function most of the bounds are found to be optimal or at least attainable. The bounds obtained here are essentially a generalization to matrix-valued, multivariate functions of the nested sequence of lens-shaped bounds in the complex plane derived by Gragg and Baker for single variable Stieltjes functions.     

Charged surfaces and the analyticity properties of the string tension in lattice gauge theories

A method to prove the fact that the string tension in strongly coupled lattice gauge theories is of the form =–log +, where is an analytic function of the inverse coupling =1/g², is presented. Its relation to random surface methods, in particular to the work of Debrushin and Holický, Kotecký, and Zahradník, is discussed.This paper is based on a talk presented at the conference on Statistical Mechanics of Phase Transitions—Mathematical and Physical Aspects, Trebon, September 1–6, 1986.     

Some results on BZ structures from Hilbertian unsharp quantum physics

Some algebraic structures determined by the class (þ) of all effects of a Hilbert space þ and by some subclasses of (þ) are investigated, in particular de Morgan-Brouwer-Zadeh posets [it is proved that (þ ⁿ )(n<) has such a structure], Brouwer-Zadeh ^* posets (a quite trivial example consisting of suitable effects is given), and Brouwer-Zadeh ³ posets which are both de Morgan and ^*.It is shown that a nontrivial class of effects of a Hilbert space exists which is a BZ ³ poset. An -preclusivity relation on the set of all vectors of þ is introduced, and it is shown that it satisfies the regularity condition also for [1/2, 1].     

The geometry of the quantum correction for topological σ-models

The ring (Frobenius algebra) of local observables for topological -models on ¹ with values in the grassmannianG(s, n) is known to be the same as the quotient of the homology ring of the target space by the (inhomogeneous) ideal generated by the so-called quantum correction. While the need for a quantum correction comes from algebraic motivations in field theory, the aim of this paper is to understand its geometric meaning. The simple examples of ^{1 n} models tell us that the quantum correction comes by restriction on the boundary of the moduli spaces which allows to compute intersections on moduli spaces of lower degrees. We will check this point of view for the case of ¹ G(s,n) models, yielding a proof of the algebraic result from physics in terms of the geometry of the -model itself.Work partially supported by National Project 40% Probabilistic and geometrical methods in Mathematical Physics and by CNR-Gruppo Nazionale di Fisica Matematica.     

Assessment of persistent-photoconductivity centers in MBE grown Al x Ga1-x as using capacitance spectroscopy measurements

Deep-level transient spectroscopy and thermally stimulated capacitance measurements were used to investigate the properties of deep traps in Si-dopedn-Al _x Ga_1–xAl layers grown by molecular beam epitaxy. Two electron traps at electron emission activation energies of 0.44 and 0.57 eV have been detected. Both traps were studied in detail and found to be the origin of the persistent-photo-conductivity phenomenon in this material. The nature of both traps is the same as of the DX center in liquid phase epitaxial material reported by Lang et al. The electron capture cross-sections are _n 1 = _n 2=8.3×10^–22cm² atT=205K. Activation energies ofE 1= 0.33eV andE 2=0.37eV at temperatures higher than 125 K were determined by DLTS measurements and by direct measurements of the capture transient. In order to allow for the variation of the free-electron concentration during the capture process, a new method for the evaluation of the electron capture crosssection was developed.     

Influence of water vapor pressure fluctuations on the spectral density of millimeter wave amplitude scintillations in an absorption region

Results are presented of scintillation spectra, measured at 54.5GHz on a 4.1 km line of sight path, when the variance of the water vapour pressure fluctuations (_e ²) is very much greater than the variance of the temperature fluctuations (_T ²). The effect of _e ² under these conditions is established both through the experimental results and the theoretical considerations which are also presented.     

Change in the electrical conductivity of organic semiconductors close to the melting point

Experimental data relating to the temperature dependence of the electrical conductivity of aromatic organic compounds are discussed within the framework of the zone (band) model. The electrical conductivity of these compounds is determined by the bond energy of the molecular compounds and diminishes with increasing melting point. The Mott formula is satisfied for anthracene, phenanthrene, and naphthalene, while the dependence of _s/_l on the change in thermal activation energy established by Gubanov for inorganic semiconductors also applies to those organic semiconductors for which is equal to or less than 2 eV. An analysis of the experimental data indicates than zone (band) theory may be used for organic semiconductors in the melting region if the character of the conductivity is similar in the solid and liquid states and the change in thermal activation energy is small.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 55–59, April, 1973.     

A refinement of Simon's correlation inequality

A general formulation is given of Simon's Ising model inequality: whereB is any set of spins separating from . We show that _b can be replaced by _{b A} whereA is the spin system insideB containing . An advantage of this is that a finite algorithm can be given to compute the transition temperature to any desired accuracy. The analogous inequality for plane rotors is shown to hold if a certain conjecture can be proved. This conjecture is indeed verified in the simplest case, and leads to an upper bound on the critical temperature. (The conjecture has been proved in general by Rivasseau. See notes added in proof.)Work partially supported by U.S. National Science Foundation grant PHY-7825390 A01     

Deuteron electrodisintegration reaction and multiquark configurations

We have obtained the cross sections d³ and d² for the ed e'pn reactions with allowance for the contribution of the six-quark state (6q) of the deuteron in its wave function. It is shown that the presence of a 6q component as an admixture of 5% can cause the cross section for deuteron electrodisintegration to increase by a factor of 1.5–2 under certain kinematical conditions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 45–50, July, 1985.In conclusion, we sincerely thank L. P. Kaptar', V. K. Luk'yanov, and A. I. Titov for numerous useful discussions and assistance in the work.     

Frictional forces and resistance to the beginning of plastic deformation in Cu-Al solid solutions

Extension curves have been obtained for Cu-Al solid solutions in the microdeformation range 10^–6-10^–3. It is shown that the dependence of the resistance to microdeformation on the degree of this deformation is described by = ₀ ⁰ + A^1/2, where ₀ ⁰ is the resistance to the beginning of plastic deformation, and A = const. The stresses _F due to frictional forces are determined from the unloading curves. The dependences of ₀ ⁰ and _F on the Al concentration c in the alloy are studied. The ₀ ⁰ = f(c) and F = (c) dependences are analyzed in the light of current ideas regarding the nature of impurity strengthening. The grain size is shown to affect the resistance to microdeformation in Cu-Al alloys.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 5, pp. 94–103, May, 1969.     

Effective stimulated emission and excited-state absorption cross-section spectra of para-phenylene-ethynylene polymers

The effective stimulated emission cross-section spectra, em,eff(), the stimulated emission cross-section spectra, em(), and the excited-state absorption cross-section spectra, ex()=em()–em,eff(), of the conjugated polymers poly(2,5-dioctadecyloxy-paraphenylene-ethynylene-co-2,5-thienyl) (OPT) and poly(2,5-dioctadecyloxy-paraphenylene-ethynylene-co-2,5-pyridinyl) (OPP) in tetrahydrofuran are determined in the fluorescence region. em,eff() determined by a fluorescence amplification technique is found to be small compared to em() indicating that ex() is nearly as large as em(). The laser excitation to the wide inhomogeneously broadened S1-absorption band leads to the formation of spectrally structured inhomogeneously broadened lattice relaxed exciton conformations extending on average over two monomer units which are thought to be responsible for upper-to-lower-state stimulated emission and lower-to-upper-state (excited-state) absorption.     

Permittivity and AC conductivity in yttria-stabilized zirconia

Alternating current (ac) conductivity and permittivity measurements were carried out on yttriastabilized cubic zirconia, with yttria varying from 9.6 to 25.5 mol%. In this composition range, the dielectric constant measured at 10³ Hz decreased from 29.8 to 23.2 as the yttria concentration increased. A plot of the ac conductivity versus frequency exhibited a plateau conductivity (_dc) and a frequency () dependent term '(). An analysis of '() with a suitable theoretical approach based on a pairs-approximation model, resulted in a calculated binding energy for the yttrium-associated oxygen vacancy of 0.29±0.05 eV, which compares favorably with values obtained by different means in previous studies. The experimental determination of the frequency dependence of the conductivity and its analysis provides an effective basis for understanding the ionic conductivity mechanism.     

Some results on the behavior and estimation of the fractal dimensions of distributions on attractors

The strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation. In this paper we first provide a rigorous mathematical framework for the study of dimension, focusing on pointwise dimension(x) and the generalized Renyi dimensionsD(q), and give a rigorous proof of inequalities first derived by Grassberger and Procaccia and Hentschel and Procaccia. We then specialize to the problem of statistical estimation of the correlation dimension and information dimension. It has been recognized for some time that the error estimates accompanying the usual procedures (which generally involve least squares methods and nearest neighbor calculations) grossly underestimate the true statistical error involved. In least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates. We then develop an estimation procedure for which corrects for an important bias term (the local measure density) and provides confidence intervals for. The general applicability of this method is illustrated with various numerical examples.