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 .     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Inequivalent quantizations for non-linear σ model

We compute the homotopy groups ₀ and ₁ of the classical configuration space of anO(3) invariant field theory on ×, where is a compact two dimensional manifold for arbitrary genusg and- denotes the time coordinate. We also present the finite dimensional, unitary, irreducible, inequivalent representations of the appropriate fundamental groups and comment on some of their implications.     

Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model

For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t ^–(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1.     

Quantum Even Spheres Σ<Superscript><Emphasis Type="Italic">2n</Emphasis></Superscript><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript> from Poisson Double Suspension

We define even dimensional quantum spheres ²ⁿ _q that generalize to higher dimension the standard quantum two-sphere of Podle and the four-sphere ⁴ _q obtained in the quantization of the Hopf bundle. The construction relies on an iterated Poisson double suspension of the standard Podle two-sphere. The Poisson spheres that we get have the same kind of symplectic foliation consisting of a degenerate point and a symplectic ²ⁿ and, after quantization, have the same C ^* –algebraic completion. We investigate their K-homology and K-theory by introducing Fredholm modules and projectors.     

К ПРОБЛЕМЕ МАГНИТНОЙ ФОКУСИРОВКИ ПУЧКОВ ЭЛЕКТРОНОВ, ЭМИТТИРО ВАННЫХ С ТЕПЛОВЫМИ СКОРОСТЯМИ

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Local energy flux and the refined similarity hypothesis

In this paper we demonstrate the locality of energy transport for incompressible Euler equations both in space and in scale. The key to the proof is the proper definition of a local subscale flux, _t (r), which is supposed to be a measure of energy transfer to length scales <l at the space point r. Kraichnan suggested that for such a quantity the refined similarity hypothesis will hold, which Kolmogorov originally assumed to hold instead for volume-averaged dissipation. We derive a local energy-balance relation for the large-scale motions which yields a natural definition of such a subscale flux. For this definition a precise form of the refined similarity hypothesis is rigorously proved as a big-O bound. The established estimate is _t (r)=O(l _3h-1) in terms of the local Hölder exponenth at the point r, which is also the estimate assumed in the Parisi-Frisch multifractal model. Our method not only establishes locality of energy transfer, but it also clarifies the physical reason that convection effects, which naively violate locality, do not contribute to the subscale flux. In fact, we show that, as a consequence of incompressibility, such effects enter into the local energy balance only as the divergence of a spatial current. Therefore, they describe motion of energy in space and cancel in the integration over volume. We also discuss theorems of Onsager, Eyink, and Constantinet al. on energy conservation for Euler dynamics, particularly to explain their relation with the Parisi-Frisch model. The Constantinet al. proof may be interpreted as giving a bound on the total flux, _t =d ^d r _t (r), of the form _t (r)=O(l _z3h-1), wherez ₃ is the third-order scaling exponent (or Besov index), in agreement with the multifractal model. Finally, we discuss how the local estimates are related to the results of Caffarelli-Kohn-Nirenberg on partial regularity for solutions of Navier-Stokes equations. They provide some heuristic support to a scenario proposed recently by Pumir and Siggia for singularities in the solutions of Navier-Stokes with small enough viscosity.     

Haag–Ruelle Scattering Theory in Presence of Massless Particles

In the Letter we investigate a q-component models on a Cayley tree. The main goal of the Letter is to develop a contour argument on Cayley tree. We define contours and study some properties of these contours. Using a contour argument we show existence of q different Gibbs measures for several q-component models.     

Investigation of the excitation of nitrogen molecules in the positive column of a discharge in a mixture of CO2 and N2

The absolute populations of the electron states of the nitrogen molecule C³_u and B³_g in the positive column of a discharge in a mixture of CO₂ and N₂ at an overall pressure of 2.5 mm Hg, a ratio of the components of 11, and a current of 60 mA, are determined. An estimate is made of the possibility of exciting the electron state C³_u by direct electron collision and by multistage excitation from the electron state B³_g. It is suggested that the most probable process by which the electron state C³_u is excited is multistage excitation from vibrational levels of the electron state B³_g.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 49–52, October, 1972.     

Interpretation of measurements of π0-meson photoproduction partial cross sections on a6Li nucleus with O+ level excitation

The anomalously large measured values of the cross section of the reaction +⁶Li ⁰ +⁶Li^* (3.56 MeV), which were obtained in two different laboratories, 260–450 MeV -rays, are discussed. It is shown that the disagreement between theory and experiment is due to the background reaction +⁷Li ⁰ + n +⁶Li^* (3.56 MeV), which became possible as a result of the poor isotropic purity of the target. This background reaction is discussed with respect to obtaining data on ⁰-meson photoproduction on neutrons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, 92–96, November, 1991.     

Inertia,relativity and cosmology

Starting with the idea that the inertia of bodies is a general property of all kinds of their potential energy, the author arrives at the two fundamental megaphysical equations (I, II)⁰ +c²=0,⁰ =0 where⁰ is the scalar gravitational potential due to the smoothed-out universe,⁰ is its electrostatic potential andc denotes the light velocity in vacuo.The first equation means physically that the cosmic potential⁰ determines uniquely the velocity of light and consequently the pseudo-Euclidean geometry in an inertial frame, in the absence of local gravitational fields. This fact implies the validity of the law of inertia in a non-empty universe only, in full agreement with Mach's principle.If we adopt, for the cosmic potential, that of Seeliger, differing from the Newtonian potential by the exponential factor exp (–r/r_g), we can use Eq. (I) to estimate the lower limit of the range r_g of gravitational interaction within the limits (10¹⁰–10¹²) light years. This suggests a steadystate model of the universe consisting of an unlimited number of finite regions (sub-universes) oscillating independently of each other. Such a superlarge-scale model universe is in agreement with the observed galactic red shift and yet it fulfils the perfect cosmological principle.     

Spinors and diffeomorphisms

We discuss the action of diffeomorphisms on spinors on an oriented manifoldM. To do this, we first describe the action of the diffeomorphism groupD(M) on the set =H ¹ (M,Z ₂) of inequivalent spin structures and show that it is affine. We argue that in the presence of spinors the gauge group of gravity is a certain double cover ofD(M) which depends on the spin structure. We explicitly compute the action ofD(M) on whenM is a closed Riemann surface; is seen to consist of exactly two orbits, corresponding to even and odd spin structures.On leave of absence from I.F.T., University of Wrocaw, Poland     

Hermiticity of Quantum Observables Versus Commutation Relations

In order to obtain sum rules and spectral representations the Hermiticity property , A = A, of observables is used. It is shown that for certain and the property turns out to be inconsistent with the commutation relations that contain A. The known Schwinger paradox is explained by this inconsistency.     

A method of integration for the inhomogeneous layer

The inhomogeneous layer of an arbitrary index profile is replaced by the conventional multilayer of homogeneous elements. When the number of layers converges to infinity, the solution is performed exactly using the method of rational functions previously described by the author. As a result the reflection coefficient is expressed as the ratio of two infinite power series in (2/)j, the coefficients being defined as multiple integrals of increasing order. The Drude formulae follow as a first approximation. The paper is dedicated to the memory of Dr. A. Vaíek, Professor of the J. E. Purkyn University in Brno, who died on November 16, 1966.     

Thermometry of an oxy-acetylene flame using multiplex degenerate four-wave mixing of C2

Thermometry of an oxy-acetylene flame using multiplex Degenerate Four-Wave Mixing (DFWM) of C₂ is demonstrated. More than 100 rotational transitions in thed ³ _g a ³ _u (0,0) Swan band of C₂ could be recorded simultaneously by use of a pulsed, broad bandwidth modeless laser. Temperatures were inferred by fitting temperature-dependent synthetic spectra of single- or multiple-shot averaged spectra. The strength and reliability of recorded signals together with the large number of rotational lines observed suggest that multiplex DFWM is a promising technique for minor species detection and for temporally resolved temperature measurements in luminous environments. Factors influencing the accuracy and precision of single-shot thermometry using the technique are discussed.     

Measurement of CrO in flames by cavity ringdown spectroscopy

CrO is an important intermediate in the high temperature oxidation chemistry of chromium containing species. This work reports the first detection of CrO in a flame. The B⁵-X⁵ electronic transition was probed by cavity ringdown spectroscopy (CRDS) in a lean (=0.38), low-pressure, flat, laminar hydrogen-oxygen-argon flame seeded with Cr(CO)₆. The previous B⁵-X⁵ CrO spectrum of Hocking et al. (605.0 nm-606.5 nm) is extended from the band head located at 605.6 nm to 614.4 nm. The temperature profiles of the doped and undoped flames were obtained from measurements of OH laser- induced fluorescence. Seeding the flame with Cr(CO)₆ increased the flame temperature by approximately 150 K. The concentration profile of CrO was measured as a function of height above the burner. CrO absorption signals were converted to concentration using the measured temperature profile and absorption cross-section calculated from lifetimes by Hedgecock et al. A lower limit peak CrO concentration of 1.6 ppb was found in the flame. Some uncertainty in the cross-section remains. Comparisons to calculations using STANJAN indicate that CrO is present in flames at super equilibrium concentrations. PACS 82.33.Vx; 42.62.Fi     

Roentgenoluminescence of hexahydrate of uranyl nitrate in phosphoric acid solution

The fluorescence (FL) and roentgenoluminescence (XRL) spectra of yellow aqueous solution of hexahydrate of uranyl nitrate phosphoric acid solution have been measured. The XRL spectrum was compared with the XRL of the green alkali alumino-phosphate glasses doped with uranium. It was shown that both the FL and XRL were due to uranyl groups. The radiative transitions are ascribed to³_1u ¹ _g ⁺ .     

Global properties of conformally flat momentum space and their implications

We consider the global structure of momentum space ^{3, 1} in a field theory which is covariant with respect to the action of global conformal group G. We show that ^{3, 1} is a homogeneous space for G which coincides with (S³×S¹)/Z₂ compact space. The radius of momentum space determines the natural invariant ultraviolet cutoff which may take the form of a Pauli-Vilars form factor in perturbation theory. We demonstrate in the case of the massless ⁴ theory how the conventional ultraviolet divergences which appear in the flat momentum space are regularized in ^{3, 1} global momentum space.     

Low-energy elementary surface excitations of symmetric films of liquid4He atT=0 K

It is known that low-energy elementary excitations of symmetric films of liquid⁴He atT=0 K are characterized by a momentum q parallel to the surface and may be described by bound states. We have evaluated wave functions and energies of these states for both best short-ranged and optimal long-ranged correlations. Quantities of physical interest may be expressed in terms of these eigenstates and, in particular, for very small momenta (q<0.2 Å^–1) they are mainly determined by the contribution due to the lowest-lying one. We propose analytic expressions for the lowest-lying excitations and fluctuations in the long-wavelength limit. It is proved that in this limiting case, the excitation energy _LW(q) and the averaged static structure functionS _LW(q) should go linearly to zero asq0, whereas the averaged direct correlationX _LW ^Dg (q) should diverge at the origin as 1/q. It is shown that numerical solutions exhibit the expected long-wavelength behavior provided that optimal correlations are used. All these results are displayed in a series of figures and are discussed in detail.     

A contribution to the theory of X-ray monochromators

The characteristic function is introduced, describing completely the monochromating effect of monochromating units. Expressions for this function are presented for monochromating units frequently used. An example of computation for Johansson's unit shows the conditions in a special case. The curves indicating the shift of the wavelength centroid of monochromated radiation for crystals of different perfection allow conclusions to be drawn about the influence of the alignment of the crystal on precision measurements of lattice constants. The experiments verify the suggested model. The computations for a given experimental arrangement permit a simple determination of the effective breadth of the reflection curve, if a distance of two suitably chosen diffraction lines of a polycrystalline specimen is measured. Finally, it was found experimentally that a small elastic bending does not essentially alter the reflection curve of highly elastic and imperfect crystals unless macroscopic distortions are present.

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The author is deeply grateful to Prof. A. Kochanovská for her encouraging interest and wishes to express his thanks to Z. Hemanová for her careful computations.