Duality-invariant orthogonality relation between the magnetic monopole and associated quark charges

Duality invariance of the Dirac-Schwinger charge-symmetric theory for electromagnetism leads one to consider the complex-valued amplitudes ₁ and ₂ for the separation between the magnetic monopole and quarks in the logarithmic charge plane. It is observed that the orthogonality relation on the latter amplitudes, Re( ₁ ^* ₂)=0, is equivalent to the equation (ln 9 ^–1)(ln 2)=(1/2) ², which is indeed satisfied by the experimental value fora to within 0.027%. In addition to fixing the unit of electric charge at a primary physical value, the orientation of ₁, ₂ may also prescribe the Cabibbo angle to have the theoretical value 12.4438.     

Compact recording of information by the holographic method

Conclusions For holography using a convergent subject beam arrangement, the effect associated with increased extrafocal information density is most pronounced when the parameter 2ac/F is small. This relationship between the object parameters (a and c) and the characteristics of the holographic system (, F) is encountered most frequently in problems of microfilming (ac) and radar imaging (ac,a ²/F is small). It is only in the case 2acF99 with an accuracy of not worse than 1%, that we can assert that the sizes of the minimal Fourier holograms will coincide.Gorkii State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 22, No. 4, pp. 449–457, April, 1979.     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

A new rigorous upper bound for the inverse critical temperature of the two-dimensional Coulomb gas

In this paper we show how to improve the recent result _c 17.2 on the inverse critical temperature for the two-dimensional Coulomb gas at low density to get the following upper bound: _c 16.     

Some properties of an “aesthetic” field theory

We continue our study of the Lorentz-invariant field theory based on the equations _jk;l ⁱ =0 and g_ij;k=0. To first order in a perturbation expansion, we find _jk;l ⁱ =0 reduces to the wave equation. In orders higher than the first, we find that _jk;l ⁱ =0 cannot be linearized. We also find that the simple wave-type equation g^ij2g/xⁱx^j=0 is contained in the theory when an appropriate choice is made for the parameters at the origin point.     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

Über den Einfluss von Stickstopf auf die Exoelektronenemission von Germanium

Zusammenfassung Es wurde der Einfluß eines Bombardements mit Stickstoffionen vor der Erregung untersucht und gezeigt, daß die Stiekstoffatome eine große Rolle bei der Entstehung des Emissionsmaximums bei 150° spielen.

---

-

, 150°C.

     

Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits

We present and discuss the derivation of a nonlinear nonlocal integrodifferential equation for the macroscopic time evolution of the conserved order parameter (r, t) of a binary alloy undergoing phase segregation. Our model is ad-dimensional lattice gas evolving via Kawasaki exchange with respect to the Gibbs measure for a Hamiltonian which includes both short-range (local) and long-range (nonlocal) interactions. The nonlocal part is given by a pair potential ^dJ(|x–y|), >0 x and y in ^d, in the limit 0. The macroscopic evolution is observed on the spatial scale ^–1 and time scale ^–2, i.e., the density (r, t) is the empirical average of the occupation numbers over a small macroscopic volume element centered atr=x. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (Part II) we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.     

The influence of successive asymmetrical magnetization reversal on the magnetic state of open samples

A study is made of the influence of successive asymmetrical magnetization reversal on the magnetic state of open samples, where the macroscopic demagnetization field has a significant effect during magnetization reversal and leads to a sort of rotation of the asymmetrical loops performed one after another. This effect is similar to reptation, which was studied experimentally by Nguyen van Dang [1–4] and theoretically explained by Néel [5, 6]. The quantitative expression of the rotation of asymmetrical loops in open samples as a function of the number of loops and amplitude of the disymmetry is similar to that with the reptation effect.

---

, , . , . .

---

---

In conclusion the authors thank Dr. L. Valenta, C. Sc., and Z. Málek, C. Sc., for valuable discussions.     

Logical independence in quantum logic

The projection latticesP(₁),P(₂) of two von Neumann subalgebras ₁, ₂ of the von Neumann algebra are defined to be logically independent if A B0 for any 0AP(₁), 0BP(₂). After motivating this notion in independence, it is shown thatP(₁),P(₂) are logically independent if ₁ is a subfactor in a finite factor andP(₁),P(₂ commute. Also, logical independence is related to the statistical independence conditions called C^*-independence W^*-independence, and strict locality. Logical independence ofP(₁,P(₂ turns out to be equivalent to the C^*-independence of (₁,₂) for mutually commuting ₁,₂ and it is shown that if (₁,₂) is a pair of (not necessarily commuting) von Neumann subalgebras, thenP(₁,P(₂ are logically independent in the following cases: is a finite-dimensional full-matrix algebra and ₁,₂ are C^*-independent; (₁,₂) is a W^*-independent pair; ₁,₂ have the property of strict locality.     

Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

The transition from the ordered commensurate phase to the incommensurate Gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields (h, v). In the (h, v) plane, the phase boundary is approached along straight lines v = k h, where (h, v) measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski–Talapov transition f const(h)^3/2 for any direction other than the tangential one. In the latter case f shows a discontinuity in the third derivative.     

Generalized Transvectants-Rankin–Cohen Brackets

We introduce o(p+1q+1)-invariant bilinear differential operators on the space of tensor densities on Rⁿ generalizing the well-known bilinear sl₂-invariant differential operators in the one-dimensional case, called Transvectants or Rankin–Cohen brackets. We also consider already known linear o(p+1q+1)-invariant differential operators given by powers of the Laplacian.     

Dielectric properties of NaCl1−xBr and KCl1−xBrx mixed ionic solution

In the present paper a three-body potential model (TBPM) has been employed for the analysis of dielectric behaviour of NaCl-NaBr and and KCl-KBr mixed crystals with varying compositions. The physical properties like dielectric constants ( ₀ and ), optic mode frequencies ( _OLO and _TO), effective charge parameter (e _s ^* ), optic mode Grüneisen parameters and strain derivatives of ₀ and dielectric constants have been calculated. The results achieved in the present study are found in fairly good agreement with the available experimental data. The results obtained by previous investigators are also shown for the sake of comparison.     

Topological aspects of Yang-Mills theory

The space of mapsS ³ G has components which give the topological quantum number of Yang-Mills theory for the groupG. Each component of the space has further topological invariants. WhenG=SU(2) we show that these invariants (the homology groups) are captured by the space of instantons. Using these invariants we show that potentials must exist for which the massless Dirac equation (in Euclidean 4-space) has arbitrarily many independent solutions (for fixed instanton number).     

The λϕ 3 4 field theory in a finite volume

The unnormalized doubly cutoff Schwinger functions converge as the ultraviolet cutoff is removed. The limits, the finite volume unnormalized Schwinger functions, are tempered distributions and areC in the coupling constant. They have asymptotic expansions given by perturbation theory. For sufficiently small they can be normalized and then they are the moments of a measure onI (IR³).Supported in part by the National Science Foundation under Grant GP 40354X.     

Averaged electron Green function and CDW pinning in one-dimensional random potential

The averaged retarded electron Green functionG ⁺(,k) in 1d disordered metal is calculated using the Berezinsky diagram technique. Using the Gorkov's theory it is shown, that the substitution of inG ⁺ (,k) by the square of the external frequency atk=0 gives the dependence of Fröhlich conductivity _F(). This dependence describes the impurity pinning of CDW in 1d disordered metals. The good agreement of this dependence with experimental data Zeller et al. about _F() in quasi-1d conductor KCP is found     

Transient soliton dynamics in perturbation fields

Transient soliton dynamics for perturbatively driven and damped sG and ⁴ solitons was found fort ^–1. The perturbed solitons remain stable with relativistic reduced time-dependent width. Internal oscillation modes of the solitons are asymptotically damped fort ^–1. There appears a relaxation regime with the field dependent superexponential relaxation of the soliton width which becomes exponential in the asymptotic regime.     

Magnetic relaxation spectrum of ferrites Mn x Fe3−x O4+γ

The initial permeability disaccommodation in ferritesMn _x Fe₃–xO₄₊ , 0·5x1, was studied in a temperature range around –200°C to +180°C. Four separate bands were found in the relaxation spectrum of these ferrites.

---

Mn _x Fe_3–x O₄₊

Mn _x Fe_3–x O₄₊ , 0,5x1, –200°C +180°C. .

     

Kinetics of random sequential parking on a line

We study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line. For the simplest fixed-length parking distribution the model reduces to the known car-parking problem and we present an alternate solution to this problem. We also consider the general homogeneous case when the parking distribution varies asx ^–1 atx 1 with the lengthx of the filling interval. We develop a scaling theory describing such mixture-deposition processes and show that the scaled hole-size distribution(), with =xt ^z a scaling variable, decays with the scaled mass as ^–exp(—const·¹⁺) as . We determine scaling exponentsz and, and find that at large times the coverage(t) has a power-law form 1 – (t)t ^–v with nonuniversal exponent =(2–)/(1+) depending on the homogeneity index .