Showing papers on "Energy (signal processing) published in 1981"

High-temperature Yang-Mills theories and three-dimensional quantum chromodynamics

Abstract: We demonstrate that for sufficiently high temperature $T$ the behavior of any four-dimensional gauge theory with small coupling constant $\ensuremath{\alpha}$, at distances beyond the electrical Debye screening length ${\ensuremath{\xi}}_{D}\ensuremath{\sim}\frac{1}{\sqrt{\ensuremath{\alpha}}T}$, is determined precisely by the corresponding three-dimensional theory. This is the magnetic sector of the original theory, and in the non-Abelian case it is a Yang-Mills theory like three-dimensional quantum chromodynamics (QC${\mathrm{D}}_{3}$). We study QC${\mathrm{D}}_{3}$ in the loop expansion, which is only valid for distances $\ensuremath{\ll}\frac{1}{\ensuremath{\alpha}T}$, in both covariant and Coulomb gauges. At a finite order in the loop expansion, the presence of logarithmic infrared divergences signals the appearance of new operators in the operator-product expansion. For example, in a covariant gauge, the gauge self-energy develops infrared divergences at two-loop order associated with the operator ${\overline{A}}^{2}$. Infrared divergences in the Wilson loop are also considered and shown to cancel below the order at which gauge-invariant local operators can appear in the operator-product expansion. The infrared structure of QC${\mathrm{D}}_{3}$ at distances $\ensuremath{\gtrsim}\frac{1}{\ensuremath{\alpha}T}$ cannot be directly probed in the loop expansion, however. We present a simpler model which is calculable in this infrared limit, and which might serve as a prototype for QC${\mathrm{D}}_{3}$. The model is massless scalar QE${\mathrm{D}}_{3}$, which with $N$ charged scalars is soluble in a $\frac{1}{N}$ expansion as $N\ensuremath{\rightarrow}\ensuremath{\infty}$. Using the $\frac{1}{N}$ expansion, we demonstrate that infrared softening occurs: the long-range behavior of the photon propagator in massless scalar QE${\mathrm{D}}_{3}$ is less singular than that of free fields. Infrared softening might also occur in QC${\mathrm{D}}_{3}$, although it cannot be demonstrated to finite order in the loop expansion. The implications of an assumed infrared softening in QC${\mathrm{D}}_{3}$ for the magnetic sector of Yang-Mills theories at high temperatures are also discussed. In particular, we consider the possibility that, if the softening is sufficiently great, there is screening of hot non-Abelian magnetic fields and possible confinement of primordial magnetic monopoles.

Energy Cost of Information Transfer

Abstract: From thermodynamic and causality considerations a general upper bound on the rate at which information can be transferred in terms of the message energy is inferred. This bound is consistent with Shannon's bounds for a band-limited channel. It prescribes the minimum energy cost for information transferred over a given time interval. As an application, a fundamental upper bound of ${10}^{15}$ operations/sec on the speed of an ideal digital computer is established.

Theory of electron-avalanche breakdown in solids

Abstract: Electron-avalanche breakdown in solids is explained by a theory that agrees with experimental results for the magnitude of the breakdown field and its temperature dependence, pulse-duration dependence, material-to-material variation, and wavelength dependence for $\ensuremath{\lambda}\ensuremath{\ge}1$ \ensuremath{\mu} m. The good agreement between experiment and theory with no parameters adjusted is obtained by using improved magnitudes and energy dependences of the electron-phonon relaxation frequencies. The contributions of both optical and acoustical phonons to electron loss and energy-space diffusion must be included. The breakdown field ${E}_{B}$ is calculated by solving an eigenvalue equation obtained from the diffusion-transport equation. Simple models and interpretations of the diffusion equation afford physical insight into breakdown and render the breakdown conditions predictable. Preliminary results indicate that the diffusion approximation fails for wavelengths considerably shorter than 1 \ensuremath{\mu} m, where multiphoton absorption must also be considered.

Analysis of Energy Flows in an lntertidal Oyster Reef

Abstract: Input-output flow analysis is adapted in a simplified manner to an intertidal oyster reef. Approximately 1 1 % of the energy moving through the reef is cycled. The largest amount of recycl~ng takes place in the detritus component. Control relat~ons are derived which imply that the filter feeders and predators have major controlling influences on energy flow in other reef components. It was first postulated by Mobius (1877) that the organisms living together on an oyster reef were functionally related to form a community or biocoenose. In the intervening period, the study of interacting groups of organisms and their concurrent environment has developed into the concept of the ecosystem. One of the interesting and comprehensive ways to increase our understanding of ecosystems is to study the flow of ene rgyha t t e r between the various components of the system and between the system and the environment. Early investigators developed simple budgets or balance sheets for ene rgyha t t e r transfers and numerous efficiency ratios were developed. In addition, because of the complexity of ecological systems the concept of trophic or feeding levels was devised by Lindeman (1942) a s a possible simplification mechanism utilizing the laws of thermodynamics. More recently, Hannon (1973) adapted the input-output theory of economics to ecosystems to reveal a 'structure' of the system by demonstrating with energy/ matter flows the direct and indirect dependence of each member of the system upon the others. Finn (1976) and Patten et al. (1976) have expanded Hannon's ideas to a formal methodology and theory for the analysis of flows in ecosystems. It is our purpose to present a new accounting of energy flux in the oyster reef system and to further develop flow analysis. O Inter-Research/Printed in F. R . Germany OYSTER REEF CONCEPTUALIZATION Oyster reefs have long been recognized as a system of organisms interacting with themselves and with their estuarine environments. Oyster reefs influence estuaries both physically by removing suspended particulate matter and changing current patterns, and biologically by removing phytoplankton and producing large quantities of oyster biomass In addition, the structure of the reef provides habitats for many estuarine organisms. In the southeastern United States, most oyster reefs are intertidal because in the high salinity estuaries of this area marine predators such as oyster drills and boring sponges decimate subtidal oyster populations (Dame, 1976). There is a tremendous amount of published and unpublished work on oysters, but the scientific literature is sparse on the oyster reef as a system. Although there is specuation on the structural and functional importance of these systems (Hedgpeth, 1957; Dame, 1976), little work has been done to synthesize existing information. The holistic approach to the analysis of ecosystems lends itself well to the synthesis and evaluation of existing data and to the development of new approaches and increased understanding of the structure and function of oyster reefs as systems. In the conceptualization of any system, it is prudent to choose a level of complexity which is justified by the 116 Mar. Ecol. Prog. Ser. 5: 115-124, 1981 Fig. 1. Intertidal oyster reef model. Flows and components are defined in Tables 1 and 2. Numbers associated with each symbol denote a to/from relationship; for example, MU61 indicates mortality by predators X6 on filter feeders X1 or a flow to X6 from X1 l available data. In the case of the oyster reef, the majority of the available information is in terms of energy units and because of this, biomass and flows will be expressed in terms of Kcal m-2 and Kcal m-2 d-l respectively. The oyster reef a s conceived here (Fig. 1) has 6 major components; filter feeders, detritus, microbiota, meiofauna, deposit feeders, and predators. The definitions and documentation of these components and the flows interconnecting them and their environment are given in Tables 1 and 2 respectively. The major components of the oyster reef are grouped according to feeding type and size. Filter feeders, deposit feeders, and predators are macroscopic organisms, while meiofauna and microbiota are progressively smaller living forms. The latter components group together diverse feeding types because little if any detailed information is available on their feeding relations. The data presented in Tables 1 and 2 and Fire 2 essentially describe an energy budget for an intertidal oyster reef in South Carolina, USA. The average annual water temperature of 20 \"C is used for the oyster reef energy budget, and temperature dependent rates of flow are converted where necessary by Q,, or graphical observation methods. For simplicity, the reef system model is assumed to obey the laws of thermodynamics and be in a steady state condition. This assumption has been supported over the past 10 years in the obsrvations of Dame (1972, 1976, 1979). This oyster reef consumes 41.5 Kcal m-2 d-' or 15,137 Kcal m-' y l , giving it one of the highest energy flows for a natural heterotrophic system. The filter feeders are the major component of the system by -I bringing energy into the reef via their coupling with the water column. This coupling allows the filter feeders to function both a s grazers of phytoplankton and as suspended particulate detritus feeders. However, there is no evidence that filter feeders in the oyster reef utilize detritus as a n energy source, but it is assumed they simply deposit this energy/matter which can then be used by other organisms. 1 I l Hi61 F i l t e r Fpdoers X 1

The local structure of the spectrum of the one-dimensional Schrödinger operator

Abstract: Let $$H_V = - \frac{{d^{\text{2}} }}{{dt^{\text{2}} }} + q(t,\omega )$$ be an one-dimensional random Schrodinger operator in ℒ2(−V,V) with the classical boundary conditions. The random potentialq(t, ω) has a formq(t, ω)=F(x t ), wherex t is a Brownian motion on the compact Riemannian manifoldK andF:K→R 1 is a smooth Morse function, $$\mathop {\min }\limits_K F = 0$$ . Let $$N_V (\Delta ) = \sum\limits_{Ei(V) \in \Delta } 1 $$ , where Δ∈(0, ∞),E i (V) are the eigenvalues ofH V . The main result (Theorem 1) of this paper is the following. IfV→∞,E 0>0,k∈Z + anda>0 (a is a fixed constant) then $$P\left\{ {N_V \left( {E_0 - \frac{a}{{2V}},E_0 + \frac{a}{{2V}}} \right) = k} \right\}\xrightarrow[{V \to \infty }]{}e^{ - an(E_0 )} (an(E_0 ))^k |k!,$$ wheren(E 0) is a limit state density ofH V ,V→∞. This theorem mean that there is no repulsion between energy levels of the operatorH V ,V→∞. The second result (Theorem 2) describes the phenomen of the repulsion of the corresponding wave functions.

Smectic, cholesteric, and Rayleigh-Benard order in two dimensions

Abstract: Order in layered smectic and cholesteric liquid-crystal films is investigated. Although long-wavelength fluctuations in the layer displacements destroy translational order at any finite tem-perature, one must also account for effects of free dislocations. The combined action of layer fluctuations and dislocations is to produce a phase at finite temperature with persistent orientational order in the local normal to the layers. At length scales greater than ${\ensuremath{\xi}}_{D}\ensuremath{\sim}\mathrm{exp}(\frac{{E}_{D}}{2{k}_{B}T})$ where ${E}_{D}$ is the energy of an isolated dislocation, the properties are those of a two-dimensional nematic, with the local layer normal playing the role of a director field. An intermediate phase of this kind could conceivably exist in bulk cholesteric liquid crystals as well. In two dimensions, an unbinding of disclination pairs eventually produces an isotropic phase. The low-temperature nematic Frank constants ${K}_{1}(T)$ and ${K}_{3}(T)$ are worked out, and compared with the diamagnetic susceptibility expected in a two-dimensional superconductor. We determine the characteristic nematic frequencies at low temperatures, using a simple model of dislocations interacting with a layer displacement field. Our analysis may also be relevant to the behavior of Rayleigh-Benard convective rolls in the presence of thermal noise fluctuations.

n , l distributions in A q + + H electron-capture collisions

Abstract: The classical-trajectory Monte Carlo method has been used to determine product-state distributions in ${A}^{q+}+\mathrm{H}\ensuremath{\rightarrow}{A}^{(q\ensuremath{-}1)+}(\mathrm{nl})+{\mathrm{H}}^{+}$ electron-capture collisions at energies 50 and 100 keV/amu for fully stripped ions in charge states $q=1 \mathrm{to} 20$. In the energy region studied, the electron-capture products are found to populate predominately principal quantum numbers around ${n}_{m}\ensuremath{\approx}{q}^{\frac{3}{4}}$. Such behavior implies the captured electron tries to preserve both its original orbital energy and dimensions after the electron-capture collision. The orbital-angular-momentum quantum numbers $l$ are more highly peaked than statistical to large $l$ values for $nl{n}_{m}$, while they are found to maximize around $l\ensuremath{\approx}{q}^{\frac{3}{4}}$ for $ng{n}_{m}$.

True Absorption and Scattering of Pions on Nuclei

Abstract: The cross section for true absorption of pions in nuclei was obtained from experiments at 85, 125, 165, 205, 245, and 315 MeV for positive pions and at 125 and 165 MeV for negative pions. The results are compared with theoretical calculations. The inclusive pion scattering angular distribution was also measured, and the results indicate that quasifree scattering plays an important role for backward scattering. The total pion-nucleus cross section is decomposed into its major channels: elastic scattering, inclusive inelastic scattering, true absorption, and single charge exchange, as a function of pion energy and charge. For light nuclei, the true absorption cross section has a strong energy dependence, reflecting the shape of the (3,3) resonance. The $A$ dependence of the true absorption cross section is much stronger than that of the inclusive inelastic scattering.NUCLEAR REACTIONS Li, C, Al, Fe, Nb, Bi (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}},{\ensuremath{\pi}}^{\ensuremath{'}}$); measured $\ensuremath{\sigma}({\ensuremath{\theta}}_{{\ensuremath{\pi}}^{\ensuremath{'}}})$, ${E}_{{\ensuremath{\pi}}^{+}}=85, 125, 165, 205, 245, \mathrm{and} 315$ MeV, ${E}_{{\ensuremath{\pi}}^{\ensuremath{-}}}=125, 165$ MeV; deduced ${\ensuremath{\sigma}}_{\mathrm{inelastic}}$, ${\ensuremath{\sigma}}_{\mathrm{absorption}}$; decomposition of ${\ensuremath{\sigma}}_{\mathrm{tot}}$.

Direct Atmospheric Forcing of Geostrophic Eddies

Abstract: To assess the role of direct stochastic wind forcing in generating oceanic geostrophic eddies we calculate analytically the response of a simple ocean model to a realistic model wind-stress spectrum and compare the results with observations The model is a continuously stratified, β-plane ocean of infinite horizontal extent and constant depth All transfer and dissipation processes are parameterized by a linear scale-independent friction law (Rayleigh damping) The model predictions that are least sensitive to this parameterization, the total eddy energy and the subsurface displacement, are in good agreement with observations in mid-ocean regions far removed from strong currents Properties that depend crucially on the parameterization of nonlinearities and topographic effects are not well reproduced Observed coherences and seasonal modulations provide direct evidence of wind forcing at high frequencies where motions have little energy Direct evidence at the more energetic low frequencies will

Off-diagonal disorder in one-dimensional systems

Abstract: We examine the nature of the zero-energy state in a one-dimensional tight-binding system with only nearest-neighbor off-diagonal disorder. We find that, although the localization length diverges at this energy, the state must nevertheless be considered as localized because the mean values of the transmission coefficient (which is directly related with the dc conductance) approach zero as the size of the system $L$ goes to infinity. In particular, we find that the geometric and harmonic mean values of the transmission coefficient behave as $\mathrm{exp}(\ensuremath{-}\ensuremath{\gamma}\sqrt{L})$, while the arithmetic mean value follows the power law ${L}^{\ensuremath{-}\ensuremath{\delta}}$ with $\ensuremath{\delta}\ensuremath{\simeq}0.50$. This is in contrast with the usual case of only diagonal disorder, where all three means behave as $\mathrm{exp}(\ensuremath{-}\ensuremath{\lambda}L)$.

Cross sections for resonant vibrational excitation of N 2 by electron impact

Abstract: We report the results of a theoretical study of resonant vibrational-excitation of ${\mathrm{N}}_{2}$ by low-energy electrons. The vibrational-excitation cross sections were calculated using ab initio fixed-nuclei resonance parameters in the complex-potential or "boomerang" model of Dub\'e and Herzenberg. The electronic resonance energy and decay width were extracted from several ab initio calculations of the $^{2}\ensuremath{\Pi}_{g}$ shape resonance of ${\mathrm{N}}_{2}^{\ensuremath{-}}$. The good agreement between the present cross sections and those obtained recently with the $R$-matrix technique indicates that the assumptions underlying the complex-potential model are valid for the case of ${{\mathrm{N}}_{2}}^{\ensuremath{-}}(^{2}\ensuremath{\Pi}_{g})$. The present results also show the sensitivity of the computed vibrational-excitation cross sections to the fixed-nuclei resonance parameters employed in the calculations. The differential vibrational-excitation cross sections at 90\ifmmode^\circ\else\textdegree\fi{} and the total integrated cross section which we have obtained agree resonably well with the available experimental data.

Quasielastic Neutrino Scattering: A Measurement of the Weak Nucleon Axial Vector Form-Factor

Abstract: The quasielastic reaction ${\ensuremath{ u}}_{\ensuremath{\mu}}n\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}p$ was studied in an experiment using the BNL 7-foot deuterium bubble chamber exposed to the wide-band neutrino beam with an average energy of 1.6 GeV. A total of 1138 quasielastic events in the momentum-transfer range ${Q}^{2}=0.06\ensuremath{-}3.00$ (${\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ were selected by kinematic fitting and particle identification and were used to extract the axial-vector form factor ${F}_{A}({Q}^{2})$ from the ${Q}^{2}$ distribution. In the framework of the conventional $V\ensuremath{-}A$ theory, we find that the dipole parametrization is favored over the monopole. The value of the axial-vector mass ${M}_{A}$ in the dipole parametrization is 1.07\ifmmode\pm\else\textpm\fi{}0.06 GeV, which is in good agreement with both recent neutrino and electroproduction experiments. In addition, the standard assumptions of conserved vector current and no second-class currents are checked.

Apparatus and method for remotely measuring temperature

Abstract: Apparatus and method for remotely measuring temperature in which a transmitter having a temperature sensitive element is placed in close proximity with the environment sought to the measured, with the temperature sensitive element controlling a reference voltage applied to a first terminal of a testing circuit, a second terminal of which receives a constant frequency alternating output of an oscillator. The output signal from the testing circuit is a constant frequency signal having a duty cycle which varies with the temperature of the element. An RF signal carrier is modulated at the transition points of the variable duty cycle signal for transmitting bursts of energy which are received and from which a replica signal corresponding to the variable duty cycle signal is reconstructed. A counter in the receiver counts high frequency pulses over a predetermined period of time during "on times" in duty cycle to obtain a numerical indication of the measured temperature.

Angular distributions of electrons elastically scattered from H 2

Abstract: Angular distributions of electrons elastically scattered from ${\mathrm{H}}_{2}$ have been measured by a crossed-beam method. Energy and angular range covered were from 2.0 to 200 eV and from -96\ifmmode^\circ\else\textdegree\fi{} to + 156\ifmmode^\circ\else\textdegree\fi{}, respectively. Comparison has been made with the previous measurements and theories. There is a good agreement above 100-eV incident energy between the previous measurements and theories and the present results, but below 100 eV considerable discrepancies exist between the previously reported results and the present measurements in the shape as well as in the magnitude of the angular distribution. The total cross sections of Golden et al. [D. E. Golden, H. W. Bandel, and J. A. Salerno, Phys. Rev. 146, 40 (1966)] above 7 eV are smaller than the present results (pure elastic) by as much as 24%, and the results of Srivastava et al. [S. K. Srivastava, A. Chutjian, and S. Trajmar, J. Chem. Phys. 63, 2659 (1975)] are also smaller than the present results by as much as 15%. The momentum-transfer cross section calculated directly from the present results of angular distribution show good agreement with those results derived from transport coefficients is swarm experiments by Frost and Phelps [L. S. Frost and A. V. Phelps, Phys. Rev. 127, 1621 (1962)] and Crompton et al. [R. W. Crompton, D. K. Gibson, and A. I. McIntosh, Aust. J. Phys. 22, 715 (1969)] below 7 eV, but not for results above 7 eV. The results of Srivastava et al. are in agreement within the experimental uncertainties above 10 eV.

Stability of time-delay systems

Abstract: This paper gives necessary and sufficient conditions for the stability of time-delay systems of the form \dot{x}(t)=A_{1}x(t)+A_{2}x(t-h) . These new conditions are derived by Lyapunov's direct method through systematic construction of the corresponding "energy" function. This function is known to exist, if a solution P_{1}(0) of the algebraic nonlinear matrix equation A_{2} =e^{[A_{1}+P_{1}(0)]h}P_{1}(0) can be determined.

Possible configurational model for hydrogen in amorphous Si:H. An exodiffusion study

Abstract: The kinetic hydrogen exodiffusion and its temperature dependence in amorphous silicon prepared by glow discharge of silane has been studied using conductivity, electron paramagnetic resonance, $^{11}\mathrm{B}\ensuremath{\rightarrow}\ensuremath{\alpha}$ nuclear reaction, and infrared absorption measurements. Comparison of the results obtained with these techniques shows the existence of two principal stages in the H exodiffusion. The hydrogen evolution for $T\ensuremath{\le}500\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ is controlled by a diffusion process with a diffusion coefficient $D$. $D$ is thermally activated; $D={D}_{0}{e}^{\frac{\ensuremath{-}{E}_{D}}{{k}_{B}T}}$ with ${D}_{0}=4.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ${\mathrm{cm}}^{2}$/${\mathrm{s}}^{\ensuremath{-}1}$ and ${E}_{D}=1.5$ eV (where ${k}_{B}$ is the Boltzmann constant). The hydrogen evolution above 500\ifmmode^\circ\else\textdegree\fi{}C is controlled by a first-order process. The activation enthalpy and entropy are, respectively, $\ensuremath{\Delta}{H}_{2}=3.4$ eV and $\ensuremath{\Delta}{S}_{2}=7.8{k}_{B}$. The fact that the EPR signal appears during the second stage and that $\ensuremath{\Delta}{H}_{2}$ is equal to the Si-H bound energy is a direct evidence that EPR signal is associated with the breaking of this bond. We then deduce an exodiffusion model assuming that hydrogen atoms can be bound in two sorts of centers. A possible configuration of H occupying such sites in the amorphous network is proposed.

Calculated electrical and thermal resistivities of Nb and Pd

Abstract: The electrical and thermal resistivities ($\ensuremath{\rho}$ and $W$) of pure Nb and Pd are calculated from nearly first principles. Realistic Korringa-Kohn-Rostoker energy bands and wave functions, experimental phonon frequencies and Born-von K\'arm\'an eigenvectors, and rigid muffin-tin electron-phonon potentials are used to generate the velocities and scattering probabilities in the Bloch-Boltzmann equation, at a mesh of nearly 48 000 points on the Fermi surface. Solutions for $\ensuremath{\rho}$ and $W$ are exhibited at three levels of accuracy: (1) the lowest-order variational approximation (LOVA) where the Fermi surface displaces rigidly; (2) the $N$-sheet approximation where different sheets of Fermi surface displace independently; (3) a fully inelastic calculation where the $N$-sheet approximation is used and the distribution function is allowed arbitrary variations with energy (normal to the Fermi surface) to reflect the inelasticity of electron-phonon scattering. Above $T=100$ K, corrections to LOVA are of order 1%, but below $T=100$ K, both the $N$-sheet approximation and inelasticity give large corrections to the LOVA results. These results are also compared with Bloch-Gr\"uneisen formulas fitted at $T\ensuremath{\sim}{\ensuremath{\Theta}}_{D}$. In the range $100 \mathrm{K}\ensuremath{\lesssim}T\ensuremath{\lesssim}300 \mathrm{K}$, calculations exceed experimental results by \ensuremath{\sim} 10%. Good agreement persists into the range $10 \mathrm{K}\ensuremath{\lesssim}T\ensuremath{\lesssim}100 \mathrm{K}$, except that in Nb theory underestimates experiment significantly at the lower-temperature end, suggesting a possible error of rigid muffin-tin models for small $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$ scattering. In Pd the interpretation is complicated by Coulomb effects. Below $T=10$ K, finite mesh size prevents reliable calculations. Simple models such as Bloch-Gr\"uneisen theory are inadequate to account for the data. Mott's (1936) "$s\ensuremath{-}d$" picture is shown to be qualitatively correct for Pd. Extension of this picture to Nb was suggested subsequently by various authors, but the present calculation does not support this.

Empirical band calculations of the optical properties of d -band metals. I. Cu, Ag, and Au

Abstract: Band-structure calculations for Rh and Pd have been performed by a second-principles approach using a combined interpolation scheme From these bands the imaginary part of the dielectric function ${\ensuremath{\epsilon}}_{2}$ in the energy range $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\le}25$ eV has been calculated with full inclusion of momentum matrix elements and spin-orbit effects The band-by-band decompositions of ${\ensuremath{\epsilon}}_{2}$ are presented, and structures are identified with transitions between specific bands in $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space Agreement with experiment is found to be good, and identifications are offered for the principal experimental structures Furthermore, ${\ensuremath{\epsilon}}_{2}$ values assuming constant matrix elements for both direct and nondirect transitions have been calculated to assess the influence of the matrix elements and to test the direct-transition model

Raman scattering studies of the impurity-induced ferroelectric phase transition in KTa O 3 :Li

Abstract: Raman scattering and optical depolarization measurements have been employed in investigations of the phase transition induced by the substitution of lithium for potassium in KTa${\mathrm{O}}_{3}$ to form ${\mathrm{K}}_{1\ensuremath{-}x}{\mathrm{Li}}_{x}\mathrm{Ta}{\mathrm{O}}_{3}$. Lithium concentrations as high as 5.4 mol% were studied. At low concentrations, $xl~0.004$, the intensities of the disorder-induced scattering features observed for pure KTa${\mathrm{O}}_{3}$ increase as the Li fraction increases. A low-frequency feature, which was previously associated with a Li resonance mode, appears to be scattering from the coupled TA and TO branches due to disorder introduced by the lithium. For $x\ensuremath{\gtrsim}0.01$, a clearly defined step in the optical depolarization is observed at a temperature ${T}_{c}$ which increases rapidly with lithium concentration and reaches a value of ${T}_{c}=70$ K at $x=0.054$. The dependence on the polarization direction of the incident light indicates that a tetragonal or orthorhombic low-temperature phase is formed with $〈100〉$ symmetry axes. New Raman-active phonons are observed near and below ${T}_{c}$. The anisotropy of the energy of the extraordinary phonon expected from polar modes is not observed in the unpoled samples. Poling can be accomplished by cooling the crystals through ${T}_{c}$ with an applied electric field, after which the polar character of these phonons is observed. The lack of anisotropy in unpoled samples is the result of the presence of ferroelectric domains with diameters smaller than optical wavelengths. Additionally, the depolarization measurements imply domain sizes of at least a few thousand \AA{}. These results clearly disagree with the previous claims that ${\mathrm{K}}_{1\ensuremath{-}x}{\mathrm{Li}}_{x}\mathrm{Ta}{\mathrm{O}}_{3}$ is not ferroelectric for $xl0.24$ and that the Li centers form a polar glass at low temperatures. Finally, the presence of the lithium impurities stiffens the TO branch at the zone center, and the ferroelectric phase results from an order-disorder transition of the off-center lithium ions.

Stability of time-delay systems

Abstract: This paper gives necessary and sufficient conditions for the stability of time-delay systems of the form \dot{x}(t)=A_{1}x(t)+A_{2}x(t-h) . These new conditions are derived by Lyapunov's direct method through systematic construction of the corresponding "energy" function. This function is known to exist, if a solution P_{1}(0) of the algebraic nonlinear matrix equation A_{2} =e^{[A_{1}+P_{1}(0)]h}P_{1}(0) can be determined.

Structure of the ground state of a fermion fluid

Abstract: Variational many-body wave functions for the ground state of liquid $^{3}\mathrm{He}$ which include triplet and backflow correlations are investigated with use of Monte Carlo integration. Our energy of - 1.9\ifmmode^\circ\else\textdegree\fi{}K removes half of the discrepancy between previous Jastrow-Slater calculations and experimental results. The first exact results for mass-three bosons are also presented. Triplet correlations in the variational wave function are equally effective in lowering the energy of both mass-three bosons and $^{3}\mathrm{He}$.

Monte Carlo Simulation of a Spin-Glass Transition

Abstract: Monte Carlo simulations show that for a system of Ruderman-Kittel-Kasuya-Yosida-coupled classical spins there exists an energy below which the system remains trapped near a single energy minimum. Provided that a small amount of anisotropy is introduced the system then exhibits, in the neighborhood of this energy, (a) a spin-glass-like peak in the susceptibility $\ensuremath{\chi}$, (b) a well-marked maximum at $\frac{{d}^{2}\ensuremath{\chi}}{d{H}^{2}}$, and (c) evidence for spin freezing at lower energies. Without anisotropy these effects are absent.

Electronic structure of transition-metal hydrides: NiH and PdH

Abstract: Ab initio self-consistent field (SCF), and configuration interaction (CI), calculations have been performed for the diatomic transition metal hydrides NiH and PdH to study the behavior of the $d$ electrons and their effect on chemical bonding. SCF calculations have been carried out for the three low-lying states, $^{2}\ensuremath{\Delta}$, $^{2}\ensuremath{\Pi}$, and $^{2}\ensuremath{\Sigma}^{+}$, which can be formed with the metal atom in the (${d}^{9}{s}^{1}$) configuration. The ground state of NiH is $^{2}\ensuremath{\Delta}$ with the $^{2}\ensuremath{\Pi}$ and $^{2}\ensuremath{\Sigma}^{+}$ states only about 0.1 eV above. In the case of PdH the $^{2}\ensuremath{\Sigma}^{+}$ state is the lowest with the $^{2}\ensuremath{\Delta}$ about 0.6 eV above. This difference can be attributed to the participation of the $4d$ electrons in the PdH bond. The $3d$ electrons in NiH seem to be more localized and "atomic $d$-like." In both cases the potential energy curves are too broad and the equilibrium bond lengths are longer than those found from spectral data. For both molecules, the CI results are considerably improved over those from the SCF calculations. However, there are still significant differences between the computed (CI) and observed values for the ground-state equilibrium bond length and force constant. Two effects are considered in order to understand these errors. For NiH, the limited CI is unable to properly account for the differential correlation energy of the $3{d}^{9}4{s}^{1}$ and $3{d}^{8}4{s}^{2}$ terms of the free Ni atom and this probably leads to the errors in the calculation. For PdH, differential atomic correlation energies are likely to be much less important, but relativistic effects are likely to be important. We have also investigated some excited states and the calculated vertical term energies are compared with experimental results.

2 s − 2 p transitions in heliumlike ions

Abstract: Precision wavelength measurements are presented for the $1s2s^{3}S_{1}\ensuremath{-}1s2p^{3}P_{0,2}$ transitions of silicon, sulfur, and chlorine. Calculations have been made for these transitions using a double expansion in ${Z}^{\ensuremath{-}1}$ and ${\ensuremath{\alpha}}^{2}{Z}^{2}$. These calculations include the nonrelativistic energy, one-electron Dirac energy, plus relativistic corrections and the Breit interaction calculated in first-order perturbation theory in both high-$Z$ and low-$Z$ approximations. After considering the one-electron Lamb-shift corrections to high order, comparison with our measurements and with other experiments for $Z=4\ensuremath{-}26$ reveals a discrepancy which is approximately $0.015{Z}^{3}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. We show that this can arise from two-electron quantum electrodynamic corrections to the one-electron Lamb shift and we derive an ab initio estimate of this correction in good agreement with the observations.

Single-particle energy levels in doped semiconductors at densities below the metal-nonmetal transition

Abstract: The single-particle density of states is calculated for a random distribution of shallow donors in semiconductors at densities below the Mott density. The donors are described within the effective-mass approximation. Calculations of the energy bands to add an electron (${D}^{\ensuremath{-}}$ band) and to remove an electron (${D}^{+}$ band) are presented in three parts: (i) At low densities, where the broadening of the ${D}^{+}$ and ${D}^{\ensuremath{-}}$ levels arises primarily from donor pairs which are closer together than the average, we have employed the donor-pair approximation to calculate the energy bands. This leads only to a small broadening in single-valley semiconductors but in a many-valley semiconductor a ${D}_{2}$ complex can have an electron affinity as large as 0.4 Ry. (ii) Next, the band edges are presented for a simple cubic lattice of donors, which would be relevant in estimating mean band positions, mobility edge, etc., in the disordered case in the intermediate doping region. The ${D}^{\ensuremath{-}}$ band is calculated using a potential derived by the method of polarized orbitals. The energy gap does not shrink appreciably until a factor of 4 below the Mott density. The energy gap is found to go to zero at a density very close to the Mott criterion (${n}_{D}^{\frac{1}{3}}{a}_{B}=0.25$) for single-valley semiconductors and at a lower density in many-valley semiconductors. (iii) Finally, to estimate the localized tail states in the many-valley case, the energies of small dense donor clusters are calculated using a local-density approximation. Because many electrons can be placed in the bonding orbitals of these clusters without violating the Pauli principle, they are found to have very large electron affinities. We find that clusters of four donors or more can attract an electron from an isolated donor. As a result there is no Mott-Hubbard gap due to correlation in many-valley semiconductors and their insulating property is due to Anderson localization. The very large fluctuations in the one-electron potential imply an Anderson transition to the metallic state.

Experimental S F 6 − / S F 6 and Cl − / CF Cl 3 Electron-Attachment Cross Sections in the Energy Range 0-200 meV

Abstract: Experimental cross sections for the electron-attachment processes for S${\mathrm{F}}_{6}^{\ensuremath{-}}$/S${\mathrm{F}}_{6}$ and ${\mathrm{Cl}}^{\ensuremath{-}}$/CF${\mathrm{Cl}}_{3}$ are reported in the energy range 0-200 meV by normalizing each attachment line shape to measurement of a thermal rate coefficient. When the same ion states are detected, good agreement is found between present values, for which a monoenergetic electron source is used, and swarm-unfolded results. The present data constitute a new limit for cross sections reported at high resolution at the lowest electron energy.

Resonant two-electron excitation in copper

Abstract: We present a calculation of the photoabsorption and photoemission cross sections of atomic copper in the neighborhood of the $3p$ threshold employing a time-dependent self-consistent-field approximation amended to include self-energy corrections necessary for a proper description of core-hole Auger decay. The calculated spectrum includes a contribution from a shake-up satellite in the two-particle spectrum which becomes resonant at the $3p\ensuremath{-}4s$ transition energy and is in good agreement with available absorption data. We present the relevant partial cross sections in the one-particle spectrum and include a brief discussion of the absorption above the $3p$ threshold with regard to the requirements of self-consistency.

Topological symmetry restoration

Abstract: We examine spontaneously broken $N$-component $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ theory at finite temperature on a static manifold whose equal-time hypersurfaces are homogeneous but may be topologically nontrivial. The alterations in the infrared structure of the field theory caused by the nontrivial topology can induce a transition from the ordered to the disordered phase, even at zero temperature. Results derived include a general expression for the zero-temperature one-loop effective potential on a topologically trivial homogeneous curved manifold and a calculation of the free energy of the self-interacting scalar field at finite temperature on a static universe whose spatial section is $\frac{{S}^{3}}{\ensuremath{\Gamma}}$, where $\ensuremath{\Gamma}$ is a discrete group.

Dynamics of phase separations of a dissipative system and a fluid mixture

Abstract: The temporal evolutions of structure functions ${S}_{k}(t)$ of quenched binary mixtures are studied theoretically. With the aid of a Langevin-type equation, basic nonlinear kinetic equations for the composition fluctuation are derived for a purely dissipative system and for a fluid mixture. Predicting that the free energy is expanded on the basis of a cluster gas picture, the equations of motion for structure functions are derived. The inverse nonhydrodynamic susceptibility ${{\ensuremath{\chi}}_{k}}^{\ensuremath{-}1}$, which is the first-derivative coefficient of the free energy, and ${S}_{k}(t)$ are assumed to have the form ${R}^{\ensuremath{-}d}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}{(\mathrm{kR})}^{\ensuremath{-}1}$ and ${R}^{d}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{S}(\mathrm{kR})$ in $d$ dimensions. Here $R$ is the average cluster diameter, which behaves as ${t}^{\ensuremath{-}{a}^{\ensuremath{'}}}$ [${a}^{\ensuremath{'}}={(d+2)}^{\ensuremath{-}1}or{(d+3)}^{\ensuremath{-}1}$ for a purely dissipative system and ${a}^{\ensuremath{'}}=\frac{l}{d}$ for a fluid mixture]. If ${{\ensuremath{\chi}}_{k}}^{\ensuremath{-}1}$ has a gap of the order ${R}^{\ensuremath{-}d}$, then our calculation of ${S}_{k}(t)$ yields good agreements with experiments (for $d=3$). The renormalizations both the mobility and of susceptibility due to long-range hydrodynamic interactions are treated with the use of the mode-coupling technique.