Two-Dimensional Coulomb Systems in a Disk with Ideal Dielectric Boundaries

We study two-dimensional Coulomb systems confined in a disk with ideal dielectric boundaries. In particular we consider the two-component plasma in detail. When the coulombic coupling constant =2 the model is exactly solvable. We compute the grand potential, densities and correlations. We show that the grand potential has a universal logarithmic finite-size correction as predicted in previous works. This logarithmic finite-size correction is also found in the free energy of another solvable model: the one-component plasma.     

Coulomb systems seen as critical systems: Ideal conductor boundaries

When a classical Coulomb system has macroscopic conducting behavior, its grand potential has universal finite-size corrections similar to the ones which occur in the free energy of a simple critical system: the massless Gaussian field. Here, the Coulomb system is assumed to be confined, by walls made of an ideal conductor material; this choice corresponds to simple (Dirichlet) boundary conditions for the Gaussian field. For ad-dimensional (d2) Coulomb system confined in a slab of thicknessW, the grand potential (in units ofk _B T) per unit area has the universal term (d/2)(d)/2^dd/2W^d–1. For a two-dimensional Coulomb system confined, in a disk of radiusR, the grand potential (in units ofk _B T) has the universal term (1/6) lnR. These results, of general validity, are checked on two-dimensional solvable models.Laboratoire Associé au Centre National de la Recherche Scientifique-URA 63.     

Self-consistent perturbation theory for dynamics of valence fluctuations

Dynamical as well as equilibrium properties of model Ce systems are investigated in both the intermediate-valence and nearly integral-valence (Kondo) regimes at finite temperatures. With self-consistent account of hybridization effects between the conduction bands and the highly correlated 4f states, the 4f-electron density of states _4f () and the dynamical magnetic susceptibility () are derived. Equilibrium properties such as the static magnetic susceptibility and the averaged 4f-electron number are also computed within the same approximation scheme that neglects intersite interactions between different Ce ions. In the intermediate-valence regime the calculated line-shape of Im ()/ is close to the Lorentzian at high temperatures, but at low temperatures there appears an inelastic peak. In the Kondo regime it is shown that a sharp peak in _4f () develops at the Fermi level as the temperature decreases. The line-shape of Im ()/ is shown to be close to the Lorentzian at all temperatures. The half-width is considerably enhanced over the Korringa value expected for the local-moment system. The temperature dependence of the half-width agrees qualitatively with experimental results in Kondo compounds such as CeB₆, CeCu₂Si₂ and CeAl₃.     

Surface Tension of an Ideal Dielectric-Electrolyte Boundary: Exactly Solvable Model

The model under consideration is a semi-infinite two-dimensional two-component plasma (Coulomb gas), stable against bulk collapse for the dimensionless coupling constant <2, in contact with a dielectric wall of dielectric constant =0. The model is mapped onto an integrable sine-Gordon theory with a free Neumann boundary condition. Using recent results on a reflection relationship between the boundary Liouville and sine-Gordon theories, an explicit expression is derived for the surface tension at a rectilinear dielectric – Coulomb gas interface. This expression reproduces the Debye-Hückel 0 limit and the exact result at the bulk collapse border, the free-fermion point =2, where the surface tension keeps a finite value. The surface collapse, identified with the divergence of the surface tension, occurs at =3.     

Power-law falloff in the kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas

We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have , whereG (x) is the two-point external charges correlation function,=dist(, Z), and for 0$$ " align="middle" border="0"> . In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0.     

Phonon assisted quantum diffusion in a periodic potential

We study the diffusion of a quantum heavy particle moving in a one dimensional strongly corrugated periodic potential, and interacting with a phonon bath.By integrating out the phonons degrees of freedom we derive an effective action functional for the particle, which includes a non-local self-interacting term whose strength is proved to be the classical friction coefficient .Using an instanton approach we express the velocity-velocity correlation function, and thus the mobility, of the brownian particle in terms of the charge density-density correlation function of a classical Coulomb gas, which in the strong corrugation limit has a very low fugacity.By making a virial expansion in the gas fugacity we evaluate the static mobility of the brownian particle as a function of the temperature, and we find two different behaviours: a diffusive behaviour at low friction, where decreases withT, and a localised behaviour at high friction, where increases withT.The cross-over between the two régimes takes place at a critical friction ₀, corresponding to the Kosterlitz-Thouless transition for the Coulomb gas.     

Some properties of a collision term of a kinetic equation in a magnetic field

The collision term of a Fokker-Planck type kinetic equation is derived for the case of a two component magnetized plasma. It is shown that the collision processes are fully described by one symmetric two-dimensional dyadicQ. The collision term is modified for the case in which the distribution function of the field particles is Maxwellian.Conditions under which the magnetic Rosenbluth potentials can be introduced are studied. It is shown, in case that the distribution function of the field particles is Maxwellian, that the coefficients of friction and diffusion are expressible in terms of two scalar potentials only if _a = 0 or if the components D and D of the difusion coefficient are constant with respect to _a , for arbitrary _b of the field particles.     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

The appearance of structure on electron energy distribution functions and its use in determining the effective cross sections of inelastic processes

The characteristics of electron energy distribution functions are investigated experimentally in a discharge with two tubular coaxially arranged electrodes, the insides of which are in the form of a grid. It is proposed to use the structure on the electron distribution functions to determine the effective cross sections of inelastic collisions, as a result of which this structure appears. The times of energy output by the electrons in the elastic and inelastic energy regions are calculated. The effective deactivation cross sections of the metastable 2³S₁ are determined in the case of second generation impacts with slow electrons, resulting in the formation of ionized helium molecules, He ₂ ⁺ , and an electron of energy 15 eV. The reasons for the appearance of structure on the electron energy distribution function is discussed.Translated from Izvestiya Uchebnykh Zavedenii Fizika, No. 11, pp. 51–62, November, 1971.     

The temperature vibrations of urea molecules

The structural and dynamic parameters of urea at 112°K and 295°K were determined by the least squares method. The characteristic temperature of the torsional optical vibrations of a molecule about a C-O bond was determined and is in good agreement with the value determined by Raman scattering. The fractional X-coordinate of the nitrogen atom corrected for torsional vibrations was determined and it was found that the magnitude of the projection of the C-N bond in the given temperature range changes only within the limits of observational errors. A new method, called temperature difference synthesis, is described and it is shown that it is suitable for rapid qualitative determination of the thermal anisotropy of the vibrations of atoms in a crystal lattice.

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112°K 295°K. C-O , , . X- , C-N . , , , .

     

К ВОПРОСУ O КРИТИЧЕСКО Й ЧАСТОТЕ ПРИ ПРЕРЫВИСТОМ ОСВЕ ЩЕНИИ

c , c n , n AgBr. .     

Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids

In a Coulomb fluid confined to a domain V, the dielectric susceptibility tensor _V depends on the shape of V, even in the thermodynamic V limit. This paper deals with the classical two-dimensional one-component plasma formulated in an elliptic V-domain, equilibrium statistical mechanics is used. For the dimensionless coupling constant =even positive integer, the mapping of the plasma onto a discrete one-dimensional anticommuting-field theory provides a new sum rule. This sum rule confirms the limiting value of _V predicted by macroscopic electrostatics and gives a finite-size correction term to _V.     

The surface layer on a ferromagnetic. The energy of some periodic domain structures

Explicit solutions are found for a number of special cases of the potential problem of periodic charge distribution. The effect of uneven distribution of the charges of a Bloch wall on the magnetostatic energy is studied, the effective width of the Bloch wall is determined, an analytical expression is found for this distribution of poles and finally the effective height of the surface layer is also determined. An expression is derived for the orientation of the vectors of magnetization in the surface layer with respect to the easy directions of magnetization. The stability of the basic domain structure up to an inclination of 6°of the plane under observation to the direction of easy magnetization and the dimensions of the domains in periodic closure structures follow from the calculations.

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. , , , , . . , 6°,, , .

     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

A Schematic Calculation of the ββ-Decay Matrix Element Within the Green Function Approach

The time integral representation of the many-body Green function describing the two-neutrino double-beta-decay (2-decay) matrix element is used in schematic calculations within the proton-neutron Lipkin model. The two-body Hamiltonian considered includes a quadratic polynomial in bosons to describe the motion of the selected degrees of freedom. The beta-transition operators also include higher-order terms in the boson expansion. They have been shown to be of crucial importance in the determination of the 2-decay matrix element M _F. We have found that in the standard QRPA approach, which exploits the form of M _F with denominator, there is a dominant unphysical contribution to M _F arising from the non-orthogonality of the initial and final quasiparticle ground states. The physical part of M _F is negligible for small values of the particle-particle interaction strength, i.e., it exhibits a different behavior as that known from the QRPA approaches.     

The distribution of ions and their valencies in manganese ferrites I. MnFe2O4+γ ferrites

A model for the distribution of cations in the spinel lattice of manganese ferrites MnFe₂O₄₊ was elaborated on the basis of the experimental studies of the basic magnetic quantities, electrical conductivity and magnetic relaxation of the given ferrites, taking into consideration their crystallographic properties. The conclusions following from this model are in good agreement with the experimental results obtained by us and by other authors both for stoichiometric manganese ferrite and for a ferrite where 0.

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I. MnFe₂O₄₊

, MnFe₂O₄₊ . , , , , , 0.

     

Changes in EPR spectrum of free radical species inγ-irradiated polyformaldehyde

We have found that gamma-irradiated polyformaldehyde does not exhibit the effect of the disappearance of the hyperfine structure of EPR spectrum as a function of the dose or the time passed since the end of irradiation, as was found earlier for a group of polymers having only C-C-C-C-atoms in the polymer chain. This difference in the change in the EPR of the polyformaldehyde (PFA) spectrum compared with the polymers with a -C-C-C-C- chain is explained by the impossibility of forming a conjugate double bond in the -C-O-C-O- chain in PFA.

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, , -, , , atom C-C-C-C-. ( ) C-C-C-C- , C-O-C-O- qu .

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The author thanks K. Vacek for many valuable discussions which helped this work.     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

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, . , . , , . , . .

     

Локалъная чувствите лъностъ фотокатодов фотоумножителей

. . .

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The local sensitivity of photo-multiplier photo-cathodes

The influence of the non-uniform distribution of the sensitivity of a photo-multiplier photo-cathode on the spectrum shape of the output pulses from a scintillation detector is studied. Methods of scanning the local sensitivity and determining its distribution function are described. The theory was compared qualitatively with measurement on a slow-neutron detector from a mixture of zinc sulphate and boric acid.

     

Spatial Spectrum of Artificial Ionospheric Irregularities Induced by Powerful HF Radiowaves

We present measurement results and spatial-spectrum shapes of the dependence of the relaxation time on the scale across the geomagnetic field for artificial ionospheric irregularities (AIIs) induced in the upper ionosphere by powerful HF radiation of the SURA heating facility. The irregularity diagnostics was based on observing amplitude scintillations of a 243-MHz beacon signal from a quasi-geostationary, solar-synchronous satellite and on measuring field-aligned scattering at frequencies 15 and 20 MHz. The satellite signal was received at the Kazan State University Observatory. The field-aligned scattering signals were received and analyzed by a bistatic HF radar based on the UTR-2 radio telescope located near Kharkov (Ukraine). It is shown that irregularities of the electron density, whose two-dimensional spectrum in the plane perpendicular to the geomagnetic field is the power law æ ^-p with index p2, are developed in the scale range 30–60 l 200–400 m. In this case, the relative fluctuations (N²)^1/2 of the electron density increase with decreasing scale l=2/æ. The estimate N²)^1/2 1–1.5% is obtained for a heating power of 150 MW and irregularity scales l 30–60 m at which the fluctuations are maximum. The measured dependence of the AII relaxation time, defined as the e-folding time of the amplitude-scintillation intensity, has the form _r l . If l 30–60 m, then the index is close to 2, whereas the effective diffusion coefficient D (2–3)· 10^-1 m²/s corresponds to the ambipolar cross-field diffusion coefficient in a magnetized plasma. The time _r for scales l 60–100 m is independent of l and increases with decreasing velocity of regular drift of the plasma. The Doppler-spectrum broadening (²)^1/2 0.6 Hz observed when receiving field-aligned scattered signals can be related to chaotic motions of plasma-density disturbances whose random drift velocities amount to (v²)^1/2 2–3 m/s for scales l 20 m at which the power-law index changes drastically.