Showing papers on "Order (ring theory) published in 1986"

Raman spectroscopy of SiO2 glass at high pressure.

Abstract: A new technique has been developed for optical studies of amorphous solids to very high pressures. Raman spectra of Si${\mathrm{O}}_{2}$ glass measured at 8 GPa indicate a significant reduction in the width of the Si-O-Si angle distribution, which has been associated with a number of anomalous properties of silica glass under ambient conditions. Between 8 and \ensuremath{\sim} 30 GPa irreversible changes in the Raman spectrum occur that are consistent with a shift in ring statistics in densified glass. The spectra suggest a breakdown in intermediate-range order at higher pressure.

Vector two-point functions in maximally symmetric spaces

Abstract: The two-point function for spinors on maximally symmetric four-dimensional spaces is obtained in terms of intrinsic geometric objects. In the massless case, Weyl spinors in anti de Sitter space can not satisfy boundary conditions appropriate to the supersymmetric models. This is because these boundary conditions break chiral symmetry, which is proven by showing that the “order parameter”\(\left\langle {\bar \psi \psi } \right\rangle \) for a massless Dirac spinor is nonzero. We also give a coordinate-independent formula for the bispinor\(S(x)\bar S(x')\) introduced by Breitenlohner and Freedman [1], and establish the precise connection between our results and those of Burges, Davis, Freedman and Gibbons [2].

Spontaneous Chiral Symmetry Breaking in Three-Dimensional QED

Abstract: A detailed analysis is given of chiral-symmetry breaking in the large-flavor (N) limit of quantum electrodynamics in (2+1) dimensions. Analytical and numerical solutions of the homogeneous Dyson-Schwinger equation for the fermion self-energy combined with a computation of the effective potential for the fermion bilinear show that it is energetically preferable for the theory to dynamically generate a mass for fermions. The magnitude of the mass is roughly exponentially suppressed in N from the fundamental dimensionful scale \ensuremath{\alpha}\ensuremath{\equiv}N ${e}^{2}$ of the gauge coupling constant, but the scale at which the self-mass begins to damp rapidly appears to be of order \ensuremath{\alpha}, so that there is no spontaneous breaking of an approximate scale invariance that the underlying theory possesses at momentum small compared to \ensuremath{\alpha}. Higher-order 1/N corrections are analyzed and it is shown that the 1/N expansion can be used consistently to demonstrate chiral-symmetry breaking. Open issues and possible improvements of the analysis are given and some avenues for future investigation suggested.

Corrections to late-stage behavior in spinodal decomposition: Lifshitz-Slyozov scaling and Monte Carlo simulations.

Abstract: The Lifshitz-Slyozov theory of the late stages of diffusion-limited spinodal decomposition (Ostwald ripening) is generalized to apply for arbitrary volume fractions of the two phases. Corrections to the asymptotic R(t)\ensuremath{\sim}${t}^{1/3}$ scaling are considered; they are due to excess transport in interfaces and are therefore of relative order ${R}^{\mathrm{\ensuremath{-}}1}$(t), where R(t) is the average domain size. That the asymptotic exponent (1/3) has not been observed in Monte Carlo simulations of Ising models can be attributed to such corrections. Further simulations of the square-lattice Ising model are performed: The results are consistent with the generalization of the Lifshitz-Slyozov theory. The recent work of Mazenko et al. that proposes instead R(t)\ensuremath{\sim}logt is criticized.

Observation of a Magnetic Antiphase Domain Structure with Long-Range Order in a Synthetic Gd-Y Superlattice

Abstract: A microscopic magnetic antiphase domain structure has been observed in a single-crystal Gd-Y superlattice by neutron diffraction. Furthermore, this long-range antiferromagnetic correlation is found to occur in a multibilayer, in which each bilayer consists of ${N}_{\mathrm{Gd}}$ ferromagnetic atomic planes of Gd followed by ${N}_{\mathrm{Y}}$ planes of nonmagnetic Y, for ${N}_{\mathrm{Y}}={N}_{\mathrm{Gd}}=10$ but not for ${N}_{\mathrm{Y}}=6 or 20$. This oscillatory behavior is consistent with recent theoretical speculation that the Gd moments are coupled through the intervening Y via the Ruderman-Kittel-Kasuya-Yosida interaction.

Excitation of the 1s5,1s4, 1s3, and 1s2 levels of argon by low-energy electrons.

Abstract: Excitation rate coefficients for the 1${s}_{5}$, 1${s}_{4}$, 1${s}_{3}$, and 1${s}_{2}$ levels of argon by collisions with low-energy electrons have been measured using a drift-tube technique. Time dependences of the absolute population densities of the excited levels were measured by an absorption method with a tunable diode laser as a light source. The absorption data were analyzed according to the rate equations for these levels and the excitation rate coefficient per unit length of electron drift and per argon-atom density was obtained for each level as a function of the electric field to gas density ratio E/N. The values for the 1${s}_{5}$ level vary from 2.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}19}$ to 2.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}17}$ ${\mathrm{cm}}^{2}$ as E/N increases from 5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}17}$ to 5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ V ${\mathrm{cm}}^{2}$. In comparison with these values, those for the 1${s}_{3}$ level are about one-fifth, those for the 1${s}_{4}$ level are about the same, and those for the 1${s}_{2}$ level are slightly larger in respective measured E/N ranges. In order to estimate the cascading effects from the higher-lying levels, excitation rate coefficients for the 2p and 3p levels have also been measured from absolute intensities of the line emissions. From a comparison of all the measured values of the excitation rate coefficients with those calculated from the Boltzmann analysis, a recommended set of cross sections for these levels has been deduced.

Fluctuating nonlinear hydrodynamics and the liquid-glass transition

Abstract: We study the fluctuating nonlinear hydrodynamics of compressible fluids. Development of the appropriate field-theoretical description for this problem requires treatment of nonlinearities which arise through the relationship g=\ensuremath{\rho}V, where g is the momentum density, \ensuremath{\rho} is the mass density, and V is the velocity field. We show how this constraint can be naturally included in a field theory of the Martin-Siggia-Rose type. We analyze the structure of the resulting field theory using the available fluctuation-dissipation theorem. We also develop the perturbation-theory expansion in powers of the temperature and evaluate the contributions from the nonlinearities to one-loop order. We show that the theory is renormalizable in the hydrodynamic limit. This field-theoretical model is used to systematically investigate the origins and viability of the nonlinear density feedback mechanism first identified by Leutheusser as a source of the liquid-glass transition. While we find that the nonlinear couplings driving this mechanism are present, we also find contributions, arising from the nonlinear constraint relating g, \ensuremath{\rho}, and V, which cut off the mechanism. The cutoff arises from a nonhydrodynamic correction not treated in previous work. While we find that there is no sharp transition, we do find evidence for a rounded version of the transition.

Structure of aggregated gold colloids.

Abstract: We report a high-resolution, small-angle x-ray study of aggregated gold colloids over the range 0.0003 to 0.08 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$. We are able to fit our data with a simple model that correctly accounts for nonfractal short-range order with a crossover to long-range fractal correlations. This provides new information on the structure of real aggregates, and new insight into the aggregation processes which lead to their formation.

Sensitivity of the Conductance of a Disordered Metal to the Motion of a Single Atom: Implications for 1 f Noise

Abstract: We show that the conductance of metals is sensitive to the motion of a single scattering center. At zero temperature and in two dimensions, the motion of one strong scattering center induces changes of the conductance of order $\frac{{e}^{2}}{h}$, independent of sample size. We discuss the implications of this result for room-temperature $\frac{1}{f}$ noise in disordered metals and we predict an anomalous low-temperature $\frac{1}{f}$ noise in metallic glasses, due to two-level systems.

Interface fluctuations in disordered systems: 5- epsilon expansion and failure of dimensional reduction.

Abstract: A functional renormalization-group $5\ensuremath{-}\ensuremath{\epsilon}$ expansion is used to calculate the exponent $\ensuremath{\zeta}$ which measures the roughness of an interface in a disorded Ising system as a function of length scale. Formal dimensional reduction is explicitly shown to break down at leading order in $\ensuremath{\epsilon}$ and field-theoretic methods fail. For random-field disorder $\ensuremath{\zeta}=\frac{\ensuremath{\epsilon}}{3}$ is obtained which resolves the discrepancy between various previous calculations; for random-bond disorder, $\ensuremath{\zeta}\ensuremath{\approx}0.2083\ensuremath{\epsilon}$ to leading order.

Spin-two fields and general covariance

Abstract: It is widely believed that all ``consistent'' theories of a spin-two field coupled to matter or nonlinearly self-coupled must be generally covariant. The extent to which this statement is true is investigated here. We consider at the classical level nonlinear equations of motion for a field ${\ensuremath{\gamma}}_{\mathrm{ab}}$ in a flat background spacetime which are derived from a Lagrangian and which reduce, in linear order, to the equations of a spin-two field. In a perturbation expansion about ${\ensuremath{\gamma}}_{\mathrm{ab}}$=0, we argue that in order for all the linearized solutions to give rise to a one-parameter family of exact solutions, the exact equations of motion must satisfy a certain type of divergence identity. (This is our ``consistency'' condition.) When the equations of motion arise from an action principle as we assume, this divergence identity implies an infinitesimal gauge invariance of the action. However, our main result is the demonstration that only a very restricted class of candidate infinitesimal gauge symmetries can actually arise from an exact (i.e., finite) gauge symmetry, as is necessary to realize the theory. Under some assumptions concerning the number of derivatives which occur in terms appearing in the divergence identity, we prove that only two types of gauge invariance are possible: (i) normal spin-two gauge invariance and (ii) general covariance. Explicit examples of nonlinear field theories of type (i) are constructed. When coupling to matter is considered, the requirement that in linear order ${\ensuremath{\gamma}}_{\mathrm{ab}}$ couple directly to the stress-energy tensor of matter may eliminate possibility (i), but I have shown this only in special cases. A similar analysis of nonlinear generalizations of the equations for a collection of spin-one fields is given, and it is shown that under analogous assumptions, the only possible type of gauge invariance for the nonlinear theory is Yang-Mills gauge invariance with respect to an arbitrary Lie algebra.

Multiple-scattering regime and higher-order correlations in x-ray-absorption spectra of liquid solutions

Abstract: By making a comparison between the Mn K-edge absorption of (${\mathrm{MnO}}_{4}$${)}^{\mathrm{\ensuremath{-}}}$ and [Mn(${\mathrm{H}}_{2}$O${)}_{6}$${]}^{2+}$ complexes in aqueous solution we obtain an experimental determination of the energy extent of the type-II multiple-scattering (MS) regime that is substantially wider than expected. Theoretical calculations based on the MS formalism support this conclusion. We also recognize three energy regions in the absorption spectra of these complexes: a full MS region, where numerous or an infinite number of MS paths of high order contribute (depending on whether the MS series converges or not), an intermediate MS region, where only a few MS paths of low order are relevant, and a single-scattering region where the photoelectron is backscattered only once by the ligands [extended x-ray-absorption fine-structure (EXAFS) regime]. Theoretical considerations show that this must be a general situation in x-ray-absorption spectra and opens the way to a unified scheme for their interpretation. The energy extent of the three regions is obviously system dependent. We also show how to generalize to MS contributions the usual EXAFS analysis using curved-wave propagators and indicate how to extract geometrical information from the spectra of the two clusters investigated. In particular the method is used to derive the Mn---O---O---Mn path length in the (${\mathrm{MnO}}_{4}$${)}^{\mathrm{\ensuremath{-}}}$ complex.

Fundamental radiation-induced defect centers in synthetic fused silicas: Atomic chlorine, delocalized E' centers, and a triplet state.

Abstract: A series of synthetic fused silicas of diverse OH contents was subjected to 100-keV x irradiations at 77 K and investigated by electron-spin-resonance techniques at \ensuremath{\sim}110 K or higher temperatures. Spectra were recorded at X-band frequencies (\ensuremath{\sim}9.2--9.3 GHz) both as the first derivative of absorption and in the high-power second-harmonic mode in order to bring out features not fully accessible by using one of these methods alone. In addition to the previously known ${E}_{\ensuremath{\alpha}}^{\mathcal{'}}$, ${E}_{\ensuremath{\gamma}}^{\mathcal{'}}$, and oxygen-associated hole centers, three new defects were detected and characterized by computer line-shape simulation methods. These were atomic chlorine, a delocalized E' center (denoted ${E}_{\ensuremath{\delta}}^{\mathcal{'}}$), and the first biradical to be reported in a-${\mathrm{SiO}}_{2}$. A sample-to-sample correlation of the radiation yields of these three new centers has been noted, leading to the suggestion that all three find their origins in specific chlorine-decorated precursor sites in the unirradiated glasses. Although significant chlorine impurities (g100 ppm) may be ubiquitous in both type-III (high OH) and type-IV (low OH) fused silicas, the occurrence of chlorine-associated radiation-induced defects appears to be anticorrelated with the OH contents of the materials. Some possible technological implications of these findings are discussed.

Polymer network of fixed topology: Renormalization, exact critical exponent gamma in two dimensions, and D=4- epsilon.

Abstract: I consider a connected self-avoiding polymer network made of identical long chains, with fixed topology. Using renormalization theory and conformal invariance, I conjecture in 2D, and give in $d=4\ensuremath{-}\ensuremath{\epsilon}$, to order $O(\ensuremath{\epsilon})$, the exact value of its critical exponent $\ensuremath{\gamma}$ as a function of the topological invariants. In 2D, the exact result fits with recent numerical data for three- and four-leg stars by Lipson et al.

Nielsen's generalized polylogarithms

Abstract: Properties (in particular functional relations and special values) of the functions \[\begin{gathered} ( - 1)^{n + p - 1} (n - 1)!p!S_{n,p} (z) = \int_0^1 {\log ^{n - 1} t\log ^p (1 - zt)\frac{{dt}} {t}} , \hfill \\ ( - 1)^{n + p - 1} (n - 1)!p!L_{n,p} (z) = \int_0^z {\log ^{n - 1} t\log ^p (1 - t)\frac{{dt}} {t}} , \hfill \\ ( - 1)^{n + p - 1} (n - 1)!p!M_{n,p} (z) = \int_0^z {\log ^{n - 1} t\log ^p (1 + t)\frac{{dt}} {t}} , \hfill \\ \end{gathered} \] which play a role in the computation of higher order radiative corrections in quantum electrodynamics, are discussed for complex z and positive integers n and p. The first function is a generalization of the well-known polylogarithms $(p = 1)$. The discussion is based on results published by Nielsen early this century in a little-known monograph.

Gradient correction in Thomas-Fermi theory.

Abstract: A new derivation of the Weizsacker-type gradient corrections to Thomas-Fermi (TF) kinetic energy functional is presented. The development is based on the first-order reduced density matrix as obtained from the one-body Green's function in the mean-path approximation devised for the purpose, using the Feynman path-integral approach; the mean-path approximation turns out to be essentially equivalent to the eikonal approximation used in quantum collision theory for high-energy collisions. This derivation agrees with the conventional gradient expansion truncated at second order, in that it gives the kinetic energy functional of the TF-(1/9)W model, that is, the sum of the original TF kinetic energy and (1/9) of the Weizsacker gradient correction. However, in the present derivation, TF-(1/9)W results from a reduced density matrix of closed form; the original TF local relation between particle, density, and one-body potential is preserved; and the kinetic energy density contains a Laplacian of particle density with a factor half of that from the gradient expansion. Most significantly, the TF-(1/9)W kinetic energy functional is the consequence of representing both the diagonal and off-diagonal elements of the density matrix correctly to zero order through the mean-path approximation to the one-body Green's function, whereas in the conventional TF approximation, the zero order of the gradient expansion, off-diagonal elements are not correct to the same order. Other results of the present approach include a nonlocal exchange energy functional of density, a one-body effective potential that contains a contribution from the kinetic energy functional derivative, and the construction of closed-form density matrices that give various kinetic energy functionals of TF-\ensuremath{\lambda}W form (justifying various existing empirical \ensuremath{\lambda} values). Also presented are the results of numerical calculation for rare-gas atoms of TFD-\ensuremath{\lambda}W models (TFD denotes Thomas-Fermi-Dirac) with \ensuremath{\lambda}=(1/3), 0.186, (1/6), and (1/9). .AE

Structure of GeSsub2 glass: Spectroscopic evidence for broken chemical order.

Abstract: Homogeneous melt-quenched (${\mathrm{Ge}}_{0.99}$${\mathrm{Sn}}_{0.01}$${)}_{\mathrm{x}}$S $_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ glasses in the glass-forming range 0lxl0.43 have been studied by scanning calorimetry, Raman, and M\"ossbauer spectroscopy. At the stoichiometric composition x=(1/3), two well-defined and chemically inequivalent $^{119}\mathrm{Sn}$ sites are observed with the site intensity ratio ${I}_{B}$/(${I}_{A}$+${I}_{B}$)=0.29(2). This ratio is found to vanish at x=0.325 and furthermore to change drastically with composition once xg(1/3). This provides evidence for chemically correlated regions in ${\mathrm{GeS}}_{2}$ glass which consist of two types of clusters---an A molecular cluster whose internal morphology is layerlike as in c-${\mathrm{GeS}}_{2}$ and a B molecular cluster whose building block consists of ethanelike ${\mathrm{Ge}}_{2}$(${\mathrm{S}}_{1/2}$${)}_{6}$ units. The 340-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ Raman band observed in ${\mathrm{GeS}}_{2}$ glass is identified as having scattering contributions from both ordered bonds: ${A}_{1}$ from the symmetric stretch of Ge(${\mathrm{S}}_{1/2}$${)}_{4}$ units; and disordered bonds: ${A}_{1g}$ mode from ${\mathrm{Ge}}_{2}$(${\mathrm{S}}_{1/2}$${)}_{6}$ units; in the Ge-rich glasses (xg(1/3)), a third type of molecular cluster, C, is populated. The internal morphology of the C cluster resembles that of c-GeS and it consists of double layers. The 250-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ Raman band, whose strength is correlated to the M\"ossbauer C sites, is identified as a double-layer breathing mode. The molecular structures of ${\mathrm{GeS}}_{2}$ and ${\mathrm{GeSe}}_{2}$ glasses are compared and contrasted.

Remarks on the Evolution of the Expanding Universe

Abstract: The relativistic energy equation for an expanding universe of non-interconverting matter and radiation is integrated. The above result, together with a knowledge of the physical conditions that prevailed during the element forming process in the early stages of the expansion, is used to determine the time dependences of proper distance as well as of the densities of matter and radiation. These relationships are employed to determine the mean galactic diameter and mass when formed as 2.1\ifmmode\times\else\texttimes\fi{}${10}^{3}$ light years and 3.8\ifmmode\times\else\texttimes\fi{}${10}^{7}$ sun masses, respectively. Galactic separations are computed to be of the order of ${10}^{6}$ light years at the present time.

Reproducibility and natural exponential families with power variance functions

Abstract: Let $X_1, \cdots, X_n$ be iid rv's having common distribution belonging to a family $\mathscr{F} = \{F_\theta: \theta \in \Theta \subset R\}$ indexed by a parameter $\theta$ $\mathscr{F}$ is said to be reproducible if there exists a sequence $\{\alpha(n)\}$ such that $\mathscr{L}(\alpha(n)\sum^n_{i=1} X_i) \in \mathscr{F}$ for all $\theta \in \Theta$ and $n = 1, 2, \cdots$ This property is investigated in connection with linear exponential families of order 1 and its intimate relationship to such families having a power variance function is demonstrated Moreover, the role of such families is examined, in a unified approach, with respect to properties relative to infinite divisibility, steepness, convolution, stability, self-decomposability, unimodality, and cumulants

Microscopic probing of order-disorder versus displacive behavior in BaTiO 3 by Fe 3 + EPR

Abstract: The cubic-crystalline field-splitting parameter a of ${\mathrm{Fe}}^{3+}$ at a Ti site in ${\mathrm{BaTiO}}_{3}$ has been measured with EPR in the cubic phase as a function of pressure p and temperature T. From these measurements, the relative explicit volume and temperature dependences of a(p,T) have been obtained. The former is three times those found in MgO, ${\mathrm{KTaO}}_{3}$, or ${\mathrm{SrTiO}}_{3}$. The relative explicit temperature dependence(\ensuremath{\partial} lna/\ensuremath{\partial}T${)}_{V}$ is positive and four and a half times that found in inert MgO. In contrast, this effect is negative in ${\mathrm{KTaO}}_{3}$ and ${\mathrm{SrTiO}}_{3}$, where soft underdamped ferroelectric modes dominate. Both giant effects in ${\mathrm{BaTiO}}_{3}$ point to a strong local Ti anharmonicity and ferroelectric order-disorder behavior in contrast to ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{KTaO}}_{3}$.

P-stability properties of runge-kutta methods for delay differential equations

Abstract: Recently the author and others have studied a class of Runge-Kutta methods for DDEs. These methods make use of certain constrained meshes, which allow to get optimal order results. In this paper we study their asymptotic stability properties, using the test equation $$\begin{gathered} y'(t) = ay(t) + by(t - \tau ),t > 0 \hfill \\ y(t) = g(t)for - \tau \leqq t \leqq 0 \hfill \\ \end{gathered} $$ wherea,b∈ℂ, σ>0, andg(t) is continuous and complex valued. It is known thaty(t)→0 ast→+∞ if |b|<-Re(a). In particular, we show that any Astable one-step collocation method for ODEs inherits the same property when it is applied to DDEs with a constrained mesh (i.e. it is P-stable).

Spanning tree formulas and chebyshev polynomials

Abstract: The Kirchhoff Matrix Tree Theorem provides an efficient algorithm for determiningt(G), the number of spanning trees of any graphG, in terms of a determinant. However for many special classes of graphs, one can avoid the evaluation of a determinant, as there are simple, explicit formulas that give the value oft(G). In this work we show that many of these formulas can be simply derived from known properties of Chebyshev polynomials. This is demonstrated for wheels, fans, ladders, Moebius ladders, and squares of cycles. The method is then used to derive a new spanning tree formula for the complete prismR n (m) =K m ×C n . It is shown that $$2^{\left( {\begin{array}{*{20}c} n \\ 2 \\ \end{array} } \right)\left( {1 - \frac{1}{{r - 1}} + o\left( 1 \right)} \right)} $$ whereT n (x) is then th order Chebyshev polynomial of the first kind.

Hadronic Contributions to Electroweak Parameter Shifts

Abstract: Usinge+e−-data, an updated analysis of hadronic contributions to electroweak parameter renormalizations is presented We emphasize the estimate of uncertainties which is important for precision tests at LEP and SLC ForMz=93 GeV and sin2Θ0=022 hadronic contributions from 5 flavors are found to be $$\Delta r_{had}^{(5)} = 00326 \pm 00007(\Delta r_{QED,had}^{(5)} = 00286 \pm 00007)$$ and $$\Delta g_{had}^{(5)} = 00602 \pm 00016(\Delta g_{3\gamma ,had}^{(5)} = 00619 \pm 00016)$$ for the renormalization of α and αg=α/sin2Θ0, respectively Parameter shifts are calculated and uncertainties due to higher order effects are estimated

Molecular-dynamics study of surface premelting effects.

Abstract: The thermodynamical and structural behavior of a (110) face of a fcc (12-6) Lennard-Jones solid has been investigated by molecular-dynamics simulation on the solid-gas coexistence line. The temperature dependence of the relevant structural and mass-transport properties shows the following. (a) Despite the high degree of disorder which gradually appears on surface layers when the temperature is increased, the surface retains its solidlike character up to temperatures (T\ensuremath{\approxeq}0.64\ensuremath{\varepsilon}/${k}_{B}$) very close to the triple point (${T}_{t}$=0.68\ensuremath{\varepsilon}/${k}_{B}$). This conclusion does not confirm the findings of previous theoretical work predicting the formation of a liquid surface layer well below the bulk melting point. (b) The large concentration of vacancy-adatom pairs, produced at the surface in the high-temperature range, accounts for the high values of the surface diffusivity. (c) The Arrhenius plot of defect concentration indicates a progressive decrease of their formation energy for temperatures ranging from ${T}_{r}$=0.8${T}_{m}$ to the melting point. Consistently, the order parameter decreases slowly with increasing temperature up to ${T}_{r}$ but from T=${T}_{r}$ to the melting point it decreases much more rapidly than predicted by the extrapolation of the low-temperature data. These results are qualitatively consistent with the onset of a surface-roughening transition, in agreement with recent experimental results obtained from helium scattering on (110) copper surfaces.

Vortices and electrically charged vortices in non-Abelian gauge theories

Abstract: Vortex solutions for a spontaneously broken SU(N) theory are explicitly constructed. N Higgs fields in the adjoint representation are needed in order to ensure topological stability. (N-1) topologically different solutions exist with magnetic flux \ensuremath{\Phi} quantized according to the relation \ensuremath{\Phi}=(2\ensuremath{\pi}/e)n/ \ensuremath{\surd}N with n=1,2,...,N-1. When a Chern-Simons term is added, the model exhibits electrically charged vortex solutions. A novel feature of these solutions is that their electric charge q is quantized in units of the fundamental charge e, q=mne/ \ensuremath{\surd}2N , with m\ensuremath{\in}Z. In addition, their angular momentum J is nonzero and also quantized, J=nm/2N.

A reduction of order two for infinite-order Lagrangians

Abstract: Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/${c}^{4}$.

Electron-electron interactions in GaAs-Al x Ga 1-x As heterostructures

Abstract: Magnetoresistance measurements are made on the two-dimensional electron gas in GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructures as a function of the sample width (W) and the potential probe spacing (L) to study the electron-electron interactions. The temperature- (T) dependent parabolic magnetoresistance, observed above 0.1 T, clearly shows the effect of electron-electron interactions. When W is large compared with ${L}_{T}$\ensuremath{\equiv}\ensuremath{\pi}(\ensuremath{\Elzxh}D/kT${)}^{1/2}$, the magnetoresistance agrees quantitatively with the two-dimensional (2D) interaction theory proposed by Altshuler and Aronov, confirming the earlier observations by Paalanen, Tsui, and Hwang. When W\ensuremath{\approxeq}${L}_{T}$, a 2D-to-1D crossover is observed. For W${L}_{T}$, the magnetoresistance agrees quantitatively with the 1D interaction theory, if boundary scattering is negligible. When L is decreased and is less than 1.8${L}_{T}$, the zero-dimensional (0D) behavior is observed, confirming the 0D interaction theory. In the narrow channels, with W less than the elastic mean-free path (${l}_{e}$), the orbital effects are greatly reduced by the boundary scattering, showing the precursor of the extremely 1D behavior. When the magnetic field is less than 0.1 T, a new size-dependent magnetoresistance is observed. This T-insensitive magnetoresistance is attributed to boundary scattering. In addition, when L\ensuremath{\approxeq}${L}_{T}$, irregular conductance fluctuations of order ${e}^{2}$/h are observed, consistent with the recent theory of Lee and Stone on universal conductance fluctuations.

Phonon-induced lifetime broadenings of electronic states and critical points in Si and Ge

Abstract: We present calculations of the lifetime broadenings of electronic states produced by the electron-phonon interaction in semiconductors and of their dependence on temperature. This effect is evaluated as a complex self-energy of the electronic states. The real part of this self-energy describes a shift of the bands with temperature, whereas the imaginary part is responsible for the broadening of the states. For the calculations based on perturbation theory to second order in atomic displacement we use a local pseudopotential with a basis of 59 plane waves, the lattice dynamics of Weber's bond-charge model, and a tetrahedron method for doubly constrained Brillouin-zone integrals. Results are given for points along the \ensuremath{\Lambda} and \ensuremath{\Delta} direction of the Brillouin zone for Si and Ge, thus obtaining the temperature dependence of the broadening parameters of the interband critical points ${E}_{0}$, ${E}_{0}^{\mathcal{'}}$, ${E}_{1}$, and ${E}_{2}$. The results are compared with experimental data obtained from ellipsometric measurements of the temperature dependence of the dielectric function. Remarkable agreement between calculated and measured data is found.

On the Frequency of Zeros of Solutions of Second Order Linear Differential Equations

Abstract: We consider the equation \(\rm f^{\prime\prime}+{A}(z){f}=0\) with linearly independent solutions f1,2, where A(z) is a transcendental entire function of finite order. Conditions are given on A(z) which ensure that max{λ(f1),λ(f2)} = ∞, where λ(g) denotes the exponent of convergence of the zeros of g. We show as a special case of a further result that if P(z) is a non-constant, real, even polynomial with positive leading coefficient then every non-trivial solution of \(\rm f^{\prime\prime}+{e}^P{f}=0\) satisfies λ(f) = ∞. Finally we consider the particular equation \(\rm f^{\prime\prime}+({e}^Z-K){f}=0\) where K is a constant, which is of interest in that, depending on K, either every solution has λ(f) = ∞ or there exist two independent solutions f1, f2 each with λ(fi) ≤ 1.

Critical behavior of the two-dimensional XY model: A Monte Carlo simulation.

Abstract: We have performed Monte Carlo (MC) simulations on systems of L\ifmmode\times\else\texttimes\fi{}L classical planar unit spins on square lattices, for L=6, 15, 30, 60, 90, and 200. The interaction between any two given spins S${\ensuremath{\rightarrow}}_{1}$ and S${\ensuremath{\rightarrow}}_{2}$ is given by -JS${\ensuremath{\rightarrow}}_{1}$\ensuremath{\cdot}S${\ensuremath{\rightarrow}}_{2}$ if ${S}_{1}$ and ${S}_{2}$ are nearest neighbors and vanishes otherwise. In order to make sure that our results correspond to equilibrium values, we have looked into the time-dependent properties of this model in the vicinity of critical temperature (${T}_{c}$). We have found that the diffusion constant for vortex motion is given at ${T}_{c}$ by D\ensuremath{\simeq}0.2 (in units of nearest-neighbor distance squared per MC step per spin). The values of the relaxation times follow from the value of D. Our computer running times were typically ${10}^{5}$ MC steps per spin, larger than any relaxation time for the system sizes we deal with. We use a procedure based on finite-size scaling to establish the value of ${T}_{c}$=0.89J/${k}_{B}$, the value of \ensuremath{ u}=0.5\ifmmode\pm\else\textpm\fi{}0.1, and the value of ${\ensuremath{\eta}}_{c}$=0.24\ifmmode\pm\else\textpm\fi{}0.03, in agreement with the values predicted by the Kosterlitz-Thouless theory.