An upper bound on the free energy for classical systems with Coulomb interactions in a varying external field

The thermodynamic limit is taken using a sequence of regions all the same shape as a given region of volume ||, with a specified distribution of normal field component on . We show that with magnetostatic interactions the limiting free energy density is bounded above by jhen where (,B) is the free energy density for a system of density in a uniform external fieldB and the inf is taken over all divergence-free fieldsB with given normal component on and all densities (x) compatible with particle number constraints of the form where _i is a sub-region of . A physical argument suggests that this upper bound is the true thermodynamic limit, and that it takes account demagnetization effects. Electrostatic interactions can be treated similarly.     

Dependence of characteristics of hysteresis loops on dislocation densities for low-alloy Cr-Mo steel

The microstructure of specimens of low-alloy Cr-Mo steel subjected to various heat treatments and various plastic deformations is studied by transmission electron microscopy. The observations indicate that the decisive factors which control the coercive forceH _c, the initial permeability _i and the Rayleigh constant are the density and the arrangement of dislocations. The precipitates have only a secondary effect. The observed linear dependencesH _c ^1/2, _i ^–1/2, ^–1 ( —dislocation density) are in full agreement with the theoretical predictions.Dedicated to Academician Vladimír Hajko on the occasion of his 65th birthday.     

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.     

Humidity dependence of the atmospheric absorption coefficient in the transparency windows centered at 0.88 and 0.73 MM

A dependence is investigated of the absorption coefficient of atmospheric water vapor on absolute air humidity in the spectral intervals =11.1+12.0 and 13.2+14.3 cm^–1 by a radiospectrometer with a multipass vacuum cell. Measurements are carried out in the humidity range 3+23 g/m³ at 140 m length of the optical path.Parts of the absorption coefficient linearly and quadratically depending on have been separately defined from the experimental data. In particular, it has been obtained for the centers of transparency windows: (=0.73mm) [dB/km]=1.68 (±0.08) +0.019 (±0.004) ², (=0.88 mm) [dB/km]=0.83 (±0.06) +0.013 (±0.002) ². The given values correspond to the temperature of 306 K and the pressure of dry air of 735 Torr.A comparison is made between our results and theoretical calculations and data of other measurements.     

The Becker-Döring cluster equations: Basic properties and asymptotic behaviour of solutions

Existence and uniqueness results are established for solutions to the Becker-Döring cluster equations. The density is shown to be a conserved quantity. Under hypotheses applying to a model of a quenched binary alloy the asymptotic behaviour of solutions with rapidly decaying initial data is determined. Denoting the set of equilibrium solutions byc ⁽⁾, 0 _s , the principal result is that if the initial density _{0 s} then the solution converges strongly toc ^(o), while if ₀ > _s the solution converges weak* toc ^(s). In the latter case the excess density ₀– _s corresponds to the formation of larger and larger clusters, i.e. condensation. The main tools for studying the asymptotic behaviour are the use of a Lyapunov function with desirable continuity properties, obtained from a known Lyapunov function by the addition of a special multiple of the density, and a maximum principle for solutions.     

Self-consistent perturbation theory for dynamics of valence fluctuations

Dynamical properties of valence-fluctuating systems are studied at absolute zero of temperature. The self-consistent perturbation theory developed for rare-earth impurity systems is used with some refinement. The theory takes account of the orthogonality catastrophe caused by hybridization of 4f and conduction electrons. Extensive numerical results are reported for the 4f-electron density of states _4f () and the dynamical magnetic susceptibility (). The results cover both the intermediate-valence and nearly integral-valence regimes of a model Ce impurity system. The present theory gives reasonable overall feature of dynamics including a sharp peak in _4f (0) in the Kondo regime. However, the low-frequency limit of dynamical quantities is not consistent with the Fermi-liquid property. It is shown that interpolation of the present results and those by the Fermi-liquid theory is possible. Hence accurate dynamical information is obtained over a wide excitation-frequency range.     

On the asymptotic behaviour of infinite gradient systems

We consider gradient systems of infinitely many particles in one-dimensional space interacting via a positive invariant pair potential with a hard core. The main assumption is that is strictly convex within the rangeR of (whereR is a fixed number ). Under some technical conditions we prove the following theorems: Let the initial distribution be given by a translation invariant point process onR ¹. Then there exists only one extreme equilibrium state with a given intensityI() satisfyingI()R ^–1, and all ergodic initial distributions with an intensityI()R ^–1 converge weakly ast to the extreme equilibrium state with the same intensity.     

There is no equivalence between ϱ′(1250) and inelastic effects in e+e−→π+π−

The analysis of all existing pion form factor data by a model respecting the fundamental principles, including (770), (1250) and (1600) contributions without inelastic effects and depending just on the physical parameters is carried out. The comparison of the obtained results with a previous analysis performed by means of a model with only (770) and (1600) contributions and inelastic effects confirmes the conclusions of Novosibirsk experimental group that the (1250) contribution and inelastic effects in e⁺e^–+– are indistinguishable. However, theoretically predicted behaviours of the P-wave isovector phase shift and the inelasticity from both models and their comparison with existing data unambiguously favour the model with (770), (1600) and inelastic contributions.We are indebted to Dr. D. Krupa who called our attention to the concise (in comparison with our original diagrammatized presentation) and transparent algebraic proof, given in the text by (30)–(33). One of us (A. Z. D.) would like to thank Professor Abdus Salam, the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics in Trieste.     

Probabilistic approach to homoclinic chaos

Three-dimensional systems possessing a homoclinic orbit associated to a saddle focus with eigenvalues ±i, – and giving rise to homoclinic chaos when the Shil'nikov condition < is satisfied are studied. The 2D Poincaré map and its 1D contractions capturing the essential features of the flow are given. At homoclinicity, these 1D maps are found to be piecewise linear. This property allows one to reduce the Frobenius—Perron equation to a master equation whose solution is analytically known. The probabilistic properties such as the time autocorrelation function of the state variablex are explicitly derived.     

More surprises in the general theory of lattice systems

I use Israel's methods to prove new theorems of ubiquitous pathology for classical and quantum lattice systems. The main result is the following: Let be any interaction and be any translation-invariant equilibrium state for (extremal or not). Then there exists a sequence { _k } of interactions converging to , having extremal (or even unique) translation-invariant equilibrium states _k , such that { _k } converges to . In certain situations the perturbations _k – can be chosen to lie in a cone of antiferromagnetic pair interactions. I discuss the connection with results of Daniëls and van Enter, and point out an application to the one-dimensional ferromagnetic Ising model with 1/r ² interaction (Thouless effect).     

A contribution to the inequality and equality relations in structure analysis

On the basis of the non-negativity for electron density in a crystal (r), the existence of inequalities and equalities between the coefficients of the Fourier expansion of the function (r) (r+t) is shown, which limits the choice of phases of the structure factors.     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

A study of the ϱ0 meson polarization in π− p reaction at 5 GeV/c

Experimental data on ⁰ meson polarization in ^– p reaction at 5 GeV/c are presented. Change in ⁰ meson polarization for mesons produced at smallP ² and atP ² 0·3 or produced in backward direction in CMS is demonstrated. Natural explanation of these phenomena is one pion exchange mechanism and mechanism of quark-antiquark annihilation as observed for ⁰ meson production in¯pp reactions.The authors are indebted to Ján Piút, Richard Lednický, V. S. Rumiancev and N. K. Koutsidi for discussions and critical comments.     

Ordering processes and activation energy in Ni3Fe-based ternary alloys

The measurement of electrical resistance () has been used, to study the kinetics of isothermal ordering in the range 200 °–545 ° C in Ni₃(FeMn) alloy quenched from 970 ° C, and the kinetics of ordering at 390 ° C in the alloy quenched from various temperatures in the 600 °–800 ° C range. The sections method and the gradient of the (t) curves were used to find the activation energy for migration and vacancy formation in this alloy on the assumption that the excess vacancies frozen in the alloy by quenching at temperatures above T_c are responsible for ordering. The activation energies for vacancy formation and migration were respectively U₀ = 33 ± 3 kilocal/mole and U_m = 39 ± 4 kilocal/mole, which in total give the activation energy for diffusion Q = 72 ± 7 kilocal/mole in the alloy studied; this approximates to the activation energy for diffusion in pure nickel.     

Dark body and black hole horizons

The formula for the horizon of a Newtonian dark body is given and compared to that of a relativistic black hole: a Newtonian dark body has at least one hair.     

Light absorption by free semiconductor carriers in the presence of a laser wave

Within the framework of the conditions ; » ^–1 ( ^–1 is the mean time of momentum relaxation), the coefficient of absorption () of a weak electromagnetic wave by the free carriers of a polar semiconductor is calculated in the presence of a strong wave (of frequency ), for arbitrary values of and . Photon absorption by band electrons is due to these latter interacting with optical phonons (of frequency _o). The problem is solved by using an analogous approach to the theory of the linear Kubo reaction. The results are valid in the absence of electron heating, when a strong wave only influences the scattering probability. The appearance of a photostimulated tail of absorption is predicted for < _o, including the jump () for ( – _o + ) ₀T as well as peaks in the function () at the points _s=s (s=1, 2, 3,...). The value (₁) is determined by the formula for the absorption coefficient for one strong wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 105–109, July, 1981.The authors are grateful to É. M. Épshtein and Sh. M. Kogan for useful discussions.     

Search for right-handed currents in muon decay

We report new limits on right-handed currents, based on precise measurements of the endpoint of the e⁺ spectrum from ⁺ decay. Highly polarized ⁺ from the TRIUMF surface beam were stopped in pure metal foils within either an 1.1-T spin-holding logitudinal field, or a 70-gauss spin-precessing transverse field. Decay e⁺ emitted within 200 mrad of the beam direction were momentum-analyzed to ±0.2%. For the spin-held data, decay via (V-A) currents requires the e⁺ rate to approach zero in the beam direction at the endpoint. Measurement of this rate sets the 90%-confidence limits P />0.9959 and M(W_R)>380 GeV, where W_R is the possible right-handed gauge boson. For the spin-precessed data we independently determine a 90% confidence limit P />0.9918.We are indebted to the entire TRIUMF management and staff for their splendid support of this experiment. In its early stages we benefited from discussion with J. Brewer, R. Cahn, K. Crowe, and W. Wenzel. Rapid commissioning of the polarimeter was made possible by the superb efforts of the LBL support staff. This research was supported in part by the U.S. Department of Energy, Division of Basic Energy Sciences, Office of Energy Research under contracts W-7405-ENG-48 and AC02-ER02289.     

Anomalous variation in electrical resistance during ordering of type Mg3Cd alloys

Using x-ray diffraction studies of the structural state of type Mg₃Cd alloys during the ordering stage accompanied by an increase in their electrical resistivity , the authors analyzed the problem of the admissibility of previously postulated interpretations of the anomalous variation in in the initial stages of ordering of certain investigated alloys. It was tentatively concluded that this anomalous variation may be associated with the nonmonotonic character of the dependence of on the degree of order.     

Synthesis and the magnetoresistance effect of layered-perovskite La<Subscript>2.5-x</Subscript>K<Subscript>0.5+x</Subscript>Mn<Subscript>2</Subscript>O<Subscript>7+δ</Subscript> (0<<Emphasis Type="Italic">x</Emphasis><0.5) polycrystals

Polycrystalline layered-perovskites La_2.5-xK_0.5+x·Mn₂O₇₊ (0<x<0.5) have been prepared by a modified sol-gel method and their structures, and magnetic and electric properties have been studied. Experimental results show that these materials exhibit ferromagnetic-to-paramagnetic phase transitions at 200, 225, 235, 247, and 253 K for x=0.05, 0.15, 0.25, 0.35, and 0.45, respectively. A large deviation between the metal-insulator transition temperature (T) and the magnetic transition temperature (T_C) is observed, and a large magnetoresistance (MR) effect with /₀ of 40% at 12 kOe is obtained over a wide temperature range. These behaviors are quite different from those observed in the well-knownABO₃-type perovskite manganites. PACS 75.30.Gw; 75.30.Et; 81.20.-n     

Some Remarks on a Nongeometrical Interpretation of Gravity and the Flatness Problem

In a nongeometrical interpretation of gravity,the metric g(x) = + (x)is interpreted as an effective metric, whereas(x) is interpreted as afundamental gravitational field, propagated in spacetime which isactually flat. Some advantages and disadvantages of suchan interpretation are discussed. The main advantage isa natural resolution of the flatness problem.