Showing papers by "International School for Advanced Studies published in 1984"

Equilibrium Geometries and Electronic Structures of Small Sodium Clusters

Abstract: We report self-consistent local-spin-density calculations which provide, for the first time, the equilibrium geometries of the sodium clusters ${\mathrm{Na}}_{n}$ and ${{\mathrm{Na}}_{n}}^{+}$ with $nl~8$ and $n=13$, without making any a priori assumptions. Our results are in excellent agreement with recently obtained photoionization appearance potentials and electron-spin-resonance spectra. We find rapid formation of the metallic bond with a dominance of closely packed structures in two and three dimensions, and propose a simple model to account for it.

Globally noncausal space-times. II. Naked singularities and curvature conditions

Abstract: In this paper we prove that if there is a naked singularity, then there will be some null geodesic, reaching ℐ+ from the singularity, which does not satisfy the strong curvature condition regardless of whether causality is violated or not. Assuming that a naked singularity is a strong curvature singularity only sufficiently far to the future, we prove that strong causality is violated arbitrarily close to ℐ+.

Scaling Behavior of Self-Avoiding Random Surfaces

Abstract: Self-avoiding random surfaces are analyzed by renormalization-group methods. The Hausdorff dimension $\frac{1}{\ensuremath{ u}}$ and the critical plaquette fugacity are computed for different dimensionalities $d$; in particular, $\ensuremath{ u}=\frac{1}{2}\ensuremath{-}\frac{\ensuremath{\epsilon}}{4}+O({\ensuremath{\epsilon}}^{2})$ for $d=2+\ensuremath{\epsilon}$. The model describes "sheet polymers" in a good solvent: A Flory type of argument yields $\ensuremath{ u}=\frac{3}{(4+d)}$, in good agreement with the renormalization results, and a critical dimensionality ${d}_{c}=8$, with $\ensuremath{ u}=\frac{1}{4}$.

Subband Structure and Landau Levels in Heterostructures

Abstract: The motion of two-dimensional carriers in quantum wells and superlattices is discussed, with emphasis on subband dispersion parallel to the interfaces and on quantization in a perpendicular magnetic field. For coupled bands (valence bands, coupled s-p bands in narrow-gap semiconductors, etc.) striking non-parabolicities of the subband dispersion and non-linearities of the Landau levels versus magnetic field occur. Results for GaAs-GaAlAs and InAs-GaSb systems are compared to analytical solutions for simple models and to experiments.

Conformation and binding of alkaline-earth dihalide molecules in an ionic model

Abstract: The paper establishes a connection, in the framework of an ionic model, between the binding of alkaline-earth dihalides in the solid phase and in the molecular phase. The polarizabilities of the metal ion and the halogen radius are identified in the model as the parameters which determine the structure of these molecules as either linear or bent, as revealed in electrical deflection experiments on molecular beams. Calculations of the molecular angle, the bond length, the binding energy and the vibrational frequencies are carried out with interionic-force laws taken over from studies of the solid alkaline-earth halides, the results being compared with the available experimental data on molecules either in the free state or embedded in a solid-krypton matrix. The analysis provides a preliminary test of interionic force models for hot-solid and liquid-structure studies.

Large scale anisotropies and polarization of the microwave background radiation in homogeneous cosmologies

Abstract: The polarization and anisotropy of the cosmological microwave background radiation on large angular scales are discussed. A quadrupole anisotropy in the expansion of the universe (shear) is considered in realistic cosmological models and the resulting anisotropies and polarization of the radiation are calculated. The role of spatial curvature is considered separately, and it is found to have two profound effects: first, in closed models only, the direction of polarization of the radiation will appear at observation to be twisted relative to the anisotropy; the existence of this twist implies that the closed universe has a handedness property. Second, in open models a quadrupole anisotropy may be distorted by the spatial curvature so that it resembles a dipole; in the extreme case all the aniso­tropy is confined to a region of small angular diameter (a ‘spot’). Following previous work by Dautcourt and Rose, a transfer equation for polarized radiation in a general curved space-time is derived. The effect of Thomson scattering by free electrons is included, and the equation is separated into those for the multipoles up to quadrupole by expanding in polynomials formed from spin-weighted spherical harmonics. A numerical integration of the equations is described, and the results are presented for the twist angle, the dipole and quadrupole anisotropies, the degree of polarization in the quadrupole mode and the ratio of polarization to quadrupole aniso­tropy in all models considered. The twist of polarization in closed models is large and should be easily observable if the polarization could be. This result suggests an important observational test of the spatial curvature of the standard models. The dipole produced in open models, due to distortion by the spatial curvature, is prominent; it appears unlikely that an intrinsic dipole to quadrupole ratio of less than unity arises in any open models in which the effect occurs when the density is below one-half the critical density. Finally, the ratio of polarization to anisotropy is expected to be a good indicator of the presence of shear, and is sensitive to the ionization history of the matter.

Structure factor of liquid alkali metals using a classical-plasma reference system

Abstract: This paper presents calculations of the liquid structure factor of the alkali metals near freezing, starting from the classical plasma of bare ions as reference liquid. The indirect ion-ion interaction arising from electronic screening is treated by an optimized random phase approximation (ORPA), imposing physical requirements as in the original ORPA scheme developed by Weeks, Chandler and Andersen for liquids with strongly repulsive core potentials. A comparison of the results with computer simulation data for a model of liquid rubidium shows that the present approach overcomes the well-known difficulties met in applying to these metals the standard ORPA based on a reference liquid of neutral hard spheres. The optimization scheme is also shown to be equivalent to a reduction of the range of the indirect interaction in momentum space, as proposed empirically in an earlier work. Comparison with experiment for the other alkalis shows that a good overall representation of the data can be obtained for sodium, potassium and cesium, but not for lithium, when one uses a very simple form of the electron-ion potential adjusted to the liquid compressibility. The small-angle scattering region is finally examined more carefully in the light of recent data of Waseda, with a view to possible refinements of the pseudopotential model.

Automated measurement of the temperature of the atmosphere at 3. 2 cm

Abstract: Concurrent with measurements of sky temperature reported in companion papers by De Amici et al., Friedman et al., Mandolesi et al., and Sironi et al, we made automated measurements of the temperature contributed by the Earth's atmosphere at 9.4 GHz (3.2-cm wavelength) every 8 min. Typical values for ${T}_{\mathrm{ATM}}$ in clear weather were 1.03\ifmmode\pm\else\textpm\fi{}0.03 K; the total range of recorded values was 0.89-1.24 K. These values were used to provide real-time atmospheric temperature corrections for the spectrum observations described in the companion papers, and to constrain models of the microwave emission of the atmosphere.

Thermodynamic properties of liquid alkali metals using a classical-plasma reference system

Abstract: We calculate the Helmholtz free energy of liquid alkali metals using variationally the one-component plasma as reference system for the structure-dependent term and simple electron theory for the structure-independent term. The various thermodynamic derivatives of the free energy are compared with data near freezing at atmospheric pressure.

Treatment of Čerenkov Radiation from electric and magnetic charges in dispersive and dissipative media

Abstract: A rigorous treatment of the problem of Cerenkov radiation from fast-moving electric and magnetic charges is presented. This is based on the rigorous solution of Maxwell's equations in a general dispersive medium possessing dielectric and magnetic properties and with, and without, dissipation. It is shown that the fields are completely determined by one scalar function. Expressions for the exact fields are obtained. From the asymptotic fields all the relevant properties of Cerenkov radiation are reproduced. In particular, it is shown that, in the absence of dissipation, the energy in each mode travels with the phase velocity of that mode. For a dissipative medium the electric field develops a longitudinal component and the energy propagates at an angle to the phase velocity. Two experiments are suggested for the experimental detection of magnetic charges and electric-dipole moments of elementary particles based upon the Cerenkov radiation which they would emit in dispersive media.

Structure of the K0.8-(KCl)0.2 liquid mixture

Abstract: The structure of liquid solutions of potassium chloride in potassium, at a concentrationx=0.2 of the salt component, is examined in an electron-ion model against multipattern neutron diffraction data. Electronic screening of long-wave-length ionic-density fluctuations and the nature of short-range ionic order are discussed. Further diffraction experiments in the small-angle scattering region and at higher concentrations of the salt component are suggested.

A correspondence between the σ-model and the Liouville model

Abstract: The σ-model and the Liouville model are both derived from a common geometrical basis. Therefore, solutions to the Liouville equation can be derived from solutions of the σ-model andvice versa. The two independent field variables in the σ-model on a coset space correspond then to two similar variables in an extended Liouville model, one being the usual «string variable», the other corresponding to a topological winding parameter. This Liouville model is finally shown to have instanton solutions of fractionally topological charge and finite energy.

Effective potential in N=1, d=4 supergravity coupled to the Volkov-Akulov field

Abstract: The one-loop effective potential is calculated for the N = 1, D = 4 supergravity theory coupled to the Volkov-Akulov field. It is then shown that after an adjustment of some of the parameters, local supersymmetry is broken and as a consequence the gravitino acquires mass through a dynamical effect.

A High Temperature Interparticle Potential for an Alternative Gauge Model

Abstract: A thermal Wilson loop for a model with two gauge fields associated with the same gauge group is discussed. Deconfinement appears at high temperature. However the colour of the deconfined matter cannot be specified.

Theory of the interface between a classical plasma and a hard wall

Abstract: The interfacial density profile of a classical one-component plasma confined by a hard wall is studied in planar and spherical geometries. The approach adapts to interfacial problems a modified hypernetted-chain approximation developed by Lado and by Rosenfeld and Ashcroft for the bulk structure of simple liquids. The specific new aim is to embody self-consistently into the theory a “contact theorem”, fixing the plasma density at the wall through an equilibrium condition which involves the electrical potential drop across the interface and the bulk pressure. The theory is brought into fully quantitative contact with computer simulation data for a plasma confined in a spherical cavity of large but finite radius. It is also shown that the interfacial potential at the point of zero charge is accurately reproduced by suitably combining the contact theorem with relevant bulk properties in a simple, approximate representation of the interfacial charge density profile.