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.     

Critical exponents and elementary particles

Particles are shown to exist for a.e. value of the mass in single phase ⁴ lattice and continuum field theories and nearest neighbor Ising models. The particles occur in the form of poles at imaginary (Minkowski) momenta of the Fourier transformed two point function. The new inequalitydm ²/dZ, where =m ₀ ² is a bare mass² andZ is the strength of the particle pole, is basic to our method. This inequality implies inequalities for critical exponents.Supported in part by the National Science Foundation under grant PHY 76-17191Supported in part by the National Science Foundation under grant MPS 75-21212     

Iteration wave function for describing the (e, 2e) spectrum of the helium atom

The wave function of the ground state of the helium atom is derived by the variational-iteration technique with the Hylleraas-Eckart momentum representation of the wave function as a first approximation. This function is used to calculate the ratios of the differential cross sections (n=2)/(n=1) and (2p)/(2s) for helium ionized by an electron impact. The calculation is conducted in the plane-wave impulse approximation for symmetric noncoplanar kinematics of the (e, 2e) process. The results are compared with previous calculations in which variational wave functions of the configurational interaction type were used. Good agreement with the existing experimental data for (n=2)/(n=1) is obtained. The results are generalized to helium ions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 45–50, December, 1986.     

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.     

The strength of Einstein's equations

The strength of Einstein's empty-space field equations is computed anew and shown to be equal to the amount of initial data required for a local solution of the equations. This same amount of initial data is shown to be precisely that required for a set of 16 unknown first-order differential equations containing 10 field variables and having six identities of second order. The 10 field variables must be functions of second order in the metric coefficients. The 16 field equationsC , = 0 whereC is Weyl's conformal tensor, are shown to have the same properties as those of the unknown equations, suggesting thatC = 0 is a satisfactory local first-order formulation of Einstein's second-order empty-space field equations.     

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   

Interpretation of the stress dependence of the steady state creep rate of Zirkaloy 4 at 873 K in terms of the knitting model

The creep rate of Zircaloy 4 has been determined as a function of strain at constant stress in the range 50 </MPa < 124. The steady state dislocation structure is a subgrain structure. The average subgrain size varies with stress as9·9G b/ (G: shear modulus,b: Burgers vector). Stress reduction tests have been performed during steady state creep to determine the static elastic modulus, the anelastic back flow and the transient creep curve caused by the stress reductions. The results are analysed in terms of the knitting model of creep. It is shown that the stress dependence of the steady state creep rate can be described by the model provided that a particle hardening term is taken into account.We thank KWU, Erlangen for providing the specimens.     

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.     

A note on product measures and representations of the canonical commutation relations

There is a well-known theorem which states that a non-zero -finite left quasi-invariant measure on a -compact locally compact groupG must be equivalent to left Haar measure. It is shown in this paper that there is a natural generalization of this fact to the case in which the groupG is replaced by a product space, one factor of which is a group. With the aid of this generalization, an easy proof of the following fact, due to H. Araki, is given: the representations of the canonical commutation relations constructed in the usual measure-theoretic manner are ray continuous.     

On the relative entropy

ForA any subset of () (the bounded operators on a Hilbert space) containing the unit, and and restrictions of states on () toA, ent _A (|)—the entropy of relative to given the information inA—is defined and given an axiomatic characterisation. It is compared with ent _A ^A (|)—the relative entropy introduced by Umegaki and generalised by various authors—which is defined only forA an algebra. It is proved that ent and ent ^S agree on pairs of normal states on an injective von Neumann algebra. It is also proved that ent always has all the most important properties known for ent ^S : monotonicity, concavity,w* upper semicontinuity, etc.     

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.     

An algebraic approach to quantum field theory and commutation relations for energy momentum in the framework of general relativity

We present a consistent set of commutation relations (C.R.) for a quantum system immersed in a classical gravitational field. The gravity field is described by metric tensorg _ik (x) andg ₀₀(x) with coordinate gaugeg _i0=0. The Hamiltonian of the system is found to be a linear function of [–g ₀₀(x)]^1/2. Its properties we define by C.R. avoiding explicit expression in terms of fields, as well as its splitting into free and interaction parts. In this way a consistent set of C.R., which are equally simple for a flat and curvilinear space, can be established. To stress the main idea of our approach, we consider the simple but still nontrivial example of a scalar electrodynamics immersed in a gravity field. The electromagnetic current operator we define by its C.R. and not explicitly. An interesting feature of this approach is that the Poisson equation follows from the consistency of the C.R. The C.R. for the energy and momentum operators of the system in a gravity field are established which generalize the usual Poincare group generators C.R. For example, we find (i/hc ²)[H _(x) ,H _(x) ]=P _– , whereH _(x) is the Hamiltonian of the system, which is a linear functional of (x)[–g ₀₀(x)]^1/2 andP _s(x) represents the momentum-density operator [averaged with the classical functions(x)].     

Interchangeability and bounds on the effective conductivity of the square lattice

The effective conductivity ^* of an infinitely interchangeable two-component random medium is considered. This class of media includes cell materials in the continuum and the bond lattice on ^d , where the cells or bonds are randomly assigned the conductivities ₁ and ₂ ( ₁, ₂ne0) with probabilitiesp ₁ andp ₂=1–p ₁. A rigorous basis for the very old and widely used low volume fraction expansion of ^* is established, by proving that ^* is an analytic function ofp ₂ in a suitable domain containing [0, 1]. In the case of the bond lattice ind=2, rigorous fourth-order upper and lower bounds on ^* valid for allp ₂, ₁, and ₂ are derived. The four perturbation coefficients entering into the bounds are obtained from the first-order volume fraction coefficient using the method of infinite interchangeability.     

Elastic and inelastic scattering of electrons by aligned light nuclei

The contribution to the elastic and inelastic scattering cross sections, , due to alignment of nuclei having axial symmetry was calculated for scattering of unpolarized, ultra-relativistic electrons by⁷Li atoms. This contribution turned out to be on the order of magnitude of the cross section ₀ previously calculated in the absence of nuclear alignment. For various nuclear orientations, the ratios /_o were calculated as a function of the momentum transfer q, which may be useful, for example, in increasing the reliability of identification of quantum numbers of nuclear states and multipole transitions.In contrast with the expression for _o, the expression for contains cross products of reduced matrix elements (RME), along with the squares of their moduli. This permits one, having previously experimentally found ₀ and under various kinematical conditions but for fixed q (the RME depend only on q), to obtain a system of equations for the RME and the statistical tensor g₂, which characterizes the degree of alignment of the nuclear target, along with the separation of the parallel and perpendicular cross sections as in the case of unaligned nuclei. Having solved the system of equations, one finds g₂ both in terms of the moduli of the RME of each multipole transition individually, and also in terms of their relative phases. The additional information thus obtained for each nuclear transition may serve as a more strict criterion for checking models of nuclei used in calculations than measurement of ₀ alone.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 94–98, January, 1990.     

Insensitivity of Quantized Hall Conductance to Disorder and Interactions

A two-dimensional quantum Hall system is studied for a wide class of potentials including single-body random potentials and repulsive electron–electron interactions. We assume that there exists a nonzero excitation gap above the ground state(s), and then the conductance is derived from the linear perturbation theory with a sufficiently weak electric field. Under these two assumptions, we prove that the Hall conductance _xy and the diagonal conductance _yy satisfy | _xy+e ² /h|const·L ^–1/2 and | _yy|const·L ^–1/12. Here e ²/h is the universal conductance with the charge –e of the electron and the Planck constant h; is the filling factor of the Landau level; and L is the linear dimension of the system. In the thermodynamic limit, our results show _xy=–e ² /h and _yy=0. The former implies that integral and fractional filling factors with a gap lead to, respectively, integral and fractional quantizations of the Hall conductance.     

Resistance to dislocation motion in copper-based solid solutions with a statistically disordered atomic distribution

The stress _F due to friction forces in copper-based solid solutions was determined. Under the conditions of the procedure used to measure _F, on the basis of the half-wave hysteresis with polycrystalline samples, the value of d: _F = _F0 + K_Fd^–(1/2) where _F0 is the resistance to dislocation motion in an alloy having an infinite grain size, and K_F is a constant. It is shown that _F0 is governed by the interaction of moving dislocations with impurity atoms in the case of a statistically disordered atomic distribution. A study was made of the effects of various factors on _F and of the nature of the changes in _F0 caused by alloying.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No.3, pp. 18–23, March, 1971.     

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.     

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.     

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     

Generalized Deformations and Hochschild Cohomology

We present a generalization of Gerstenhaber's theory of deformations. We no longer assume that the deformation parameter t acts in its usual free and symmetric way on the elements of the original algebra A, but in the following manner: t · a = (a)t and a · t = (a)t, where and are endomorphisms of A. We develop the cohomological framework adapted to these deformations.