Showing papers on "Field (physics) published in 1969"

Power spectrum of light scattered by two-level systems

Abstract: The power spectrum of the light scattered by a two-level atom driven near resonance by a monochromatic classical electric field is evaluated. The atom is assumed to relax to equilibrium with the driving field via radiation damping, which is treated by explicitly coupling the atom to the quantized electromagnetic field modes. The power spectrum of the scattered field is directly obtainable from the two-time atomic dipole moment correlation function, which is evaluated by a method based on a Markoff-type assumption analogous to that used to evaluate the time evolution of single-time atomic expectation values.

Structure of phenomenological lagrangians. ii.

Abstract: The general method for constructing invariant phenomenological Lagrangians is described. The fields are assumed to transform according to (nonlinear) realizations of an internal symmetry group, given in standard form. The construction proceeds through the introduction of covariant derivatives, which are standard forms for the field gradients. The case of gauge fields is also discussed.

A model of interplanetary and coronal magnetic fields.

Abstract: Green function solution to Maxwell equations for interplanetary and coronal magnetic fields above photosphere, considering field at source surface

Quantized Fields and Particle Creation in Expanding Universes. I

Abstract: Spin-0 fields of arbitrary mass and massless fields of arbitrary spin are considered. The equations governing the fields are the covariant generalizations of the special-relativistic free-field equations. The metric, which is not quantized, is that of a universe with an expanding (or contracting) Euclidean 3-space. The spin-0 field of arbitrary mass is quantized in the expanding universe by the canonical procedure. The quantization is consistent with the time development dictated by the equation of motion only when the boson commutation relations are imposed. This consistency requirement provides a new proof of the connection between spin and statistics. We show that the particle number is an adiabatic invariant, but not a strict constant of the motion. We obtain an expression for the average particle density as a function of the time, and show that particle creation occurs in pairs. The canonical creation and annihilation operators corresponding to physical particles during the expansion are specified. Thus, we do not use an $S$-matrix approach. We show that in a universe with flat 3-space containing only massless particles in equilibrium, there will be precisely no creation of massless particles as a result of the expansion, provided the Einstein field equations without the cosmological term are correct. Furthermore, in a dust-filled universe with flat 3-space there will be precisely no creation of massive spin-0 particles in the limit of infinite mass, again provided that the Einstein field equations are correct. Conversely, without assuming any particular equations, such as the Einstein equations, as governing the expansion of the universe, we obtain the familiar Friedmann expansions for the radiation-filled and the dust-filled universes with flat 3-space. We only make a very general and natural hypothesis connecting the particle creation rate with the macroscopic expansion of the universe. In one derivation, we assume that in an expansion of the universe in which a particular type of particle is predominant, the type of expansion approached after a long time will be such as to minimize the average creation rate of that particle. In another derivation, we use the assumption that the reaction of the particle creation back on the gravitational field will modify the expansion in such a way as to reduce, if possible, the creation rate. This connection between the particle creation and the Einstein equations is surprising because the Einstein equations themselves played no part at all in the derivation of the equations governing the particle creation. Finally, on the basis of a so-called infinite-mass approximation, we argue that in the present predominantly dust-filled universe, only massless particles of zero spin might possibly be produced in significant amounts by the present expansion. In this connection, we show that massless particles of arbitrary nonzero spin, such as photons or gravitons, are not created by the expansion, regardless of its form.

A circular-harmonic computer analysis of rectangular dielectric waveguides

Abstract: This paper describes a computer analysis of the propagating modes of a rectangular dielectric waveguide. The analysis is based on an expansion of the electromagnetic field in terms of a series of circular harmonics, that is, Bessel and modified Bessel functions multiplied by trigonometric functions. The electric and magnetic fields inside the waveguide core are matched to those outside the core at appropriate points on the boundary to yield equations which are then solved on a computer for the propagation constants and field configurations of the various modes. The paper presents the results of the computations in the form of curves of the propagation constants and as computer generated mode patterns. The propagation curves are presented in a form which makes them refractive-index independent as long as the difference of the index of the core and the surrounding medium is small, the case which applies to integrated optics. In addition to those for small index difference, it also gives results for larger index differences such as might be encountered for microwave applications.

Noncausality and Other Defects of Interaction Lagrangians for Particles with Spin One and Higher

Abstract: We analyze critically what happens when various interaction terms are added to a Lagrangian describing a free particle with spin \ensuremath{\ge}1. Good behavior results when the charged spin-one particle is coupled minimally to an external electromagnetic field or via a magnetic dipole moment. However, with an arbitrary electric quadrupole moment, the spin-one particle propagates noncausally ($vgc$) in an electrostatic field. Noncausal behavior is also found for the neutral vector field with self-coupling $\ensuremath{\lambda}{({W}_{\ensuremath{\mu}}{W}^{\ensuremath{\mu}})}^{2}$. Another kind of disease appears when the spin-two particle is given a charge: A constraint is converted into an equation of motion, so that there are six degrees of freedom instead of the desired five.

The response of pinned flux vortices to low-frequency fields

Abstract: The susceptibility of type II superconductors in low-frequency alternating current fields has been measured using a phase sensitive detector. Penetrations of magnetic field of between 300 A and 500 μm can be measured and if it is assumed that a critical state exists the field profile across the specimen can be plotted on this scale. The response is linear at low amplitude and is consistent with a model based on the reversible oscillation of vortices in harmonic wells. It is not consistent with the signal predicted from `flux creep'. The effective potential wells are found to be harmonic up to their edges and only about 25 A in radius. The resolution is sufficient to show that the surface current is not a critical state, but can be described by a single row of vortices pinned by the boundary of the specimen.

Theory of Electronic States and Transport in Graded Mixed Semiconductors

Abstract: Semiconductors which are slowly graded in composition can be shown to have position-dependent band gaps and position-dependent effective masses, describable in terms of an effective Hamiltonian in an effective-mass equation. The effective Hamiltonian previously obtained is, in the present work, rendered Hermitian. Electronic minority-carrier transport for graded systems is described in terms of an effective field which includes the electrostatic field plus a term in the gradient of the band edge and another in the gradient of the effective mass. The local radiative-recombination lifetime and local density of states for inhomogeneous semiconductors are discussed. The equation for the excess minority-carrier concentration in an inhomogeneous semiconductor is deduced and is found to differ from that in an homogeneous system, by the effective field replacing the electric field, by the position dependences of lifetime and mobility, and by terms in the mobility gradient. Some phenomena specific to graded mixed semiconductors are considered on the basis of the theoretical analysis.

Influence of Electric Fields on the Molecular Alignment in the Liquid Crystal p-(Anisalamino)-phenyl Acetate

Abstract: The effects of electric fields on the molecular alignment in the liquid crystal p-(anisalamino)-phenyl acetate are discussed The behavior of this material is similar to that of p-azoxyanisole in that the ordering which is normally observed shows an alignment with the molecular axis preferring a direction parallel to the field at low audio frequencies, and perpendicular to the field for frequencies of a few hundred kHz Results comparing the effectiveness of electric and magnetic fields for producing molecular alignment are presented which support a theory presented earlier to explain the ordering in p-azoxyanisole at audio frequencies This theory involves the anisotropy associated with the electrical conductivity Results are also presented which show that the effectiveness of dc electric fields is comparable to that for low audio frequencies A few comments are made concerning recent work employing electric fields to produce ordering in liquid crystals for NMR studies

Distortion of a cholesteric structure by a magnetic field

Abstract: An experiment is described which confirms the theory of the distortion of a cholesteric structure by a magnetic field. Field effects in a sample of p‐azoxyanisole doped with cholesteryl acetate were viewed directly with a microscope, and the pitch of the helical structure was measured as a function of field strength.

Field-aligned currents in the magnetosphere.

Abstract: Certain satellite and terrestrial observations of transient magnetic fluctuations show a high degree of localization, while other observations are of a definite worldwide character. The worldwide fluctuations in the magnetic field are probably well explained in terms of hydromagnetic waves propagating through the magnetosphere in modes with the wave polarization current flowing perpendicular to the geomagnetic field. However, for the localized fluctuations such an interpretation is inconsistent with present theory of hydromagnetic wave propagation in the magnetosphere. We suggest that the observations of localized magnetic fluctuations might be better interpreted in terms of field-aligned currents in the magnetosphere.

Theory of Electron Diffusion Parallel to Electric Fields. I. Theory

Abstract: Recent experimental results in many gases demonstrate that the apparent rate of electron diffusion parallel to an electric field can differ significantly from that in the perpendicular direction. We have explained this anomalous behavior by taking account of the effect of electron density gradients on the solution of the Boltzmann equation representing a pulse of electrons under the influence of a uniform electric field. When the electron collision frequency increases with energy, the theory predicts that the leading edge of the pulse has a reduced mobility because of a higher-average electron speed and collision rate. Similarly the mobility of the trailing edge is enhanced, and consequently the half width of the pulse in the field direction is characterized by a new diffusion coefficient. The ratio of the longitudinal diffusion coefficient to the transverse diffusion coefficient is given as integrals involving the momentum transfer cross section and the unperturbed energy distribution. This ratio at high electric fields is found to be approximately one-half and one-fifth, for momentum transfer cross sections that are independent of and linearly proportional to the electron energy.

Solutions of the Zero-Rest-Mass Equations

Abstract: By means of contour integrals involving arbitrary analytic functions, general solutions of the zero‐rest‐mass field equations in flat space‐time can be generated for each spin. If the contour surrounds only a simple (respectively, low‐order) pole of the function, the resulting field is null (respectively, algebraically special).

On Growth Poles

Abstract: Perroux argued that economic space as an abstract field of forces leads to the notion of a vector of economic forces, and hence to the concept of growth poles.His further view that economic develop...

Superconductivity in a Molecular Field. I

Abstract: The Fulde-Ferrel model, in which a molecular field is acting on the spins of the con­ duction electrons responsible for supercond,uctivity, is investigated. The superconducting state, that is described by the condensate wave function oscillating in space and gives rise to a gapless energy spectrum, is shown to be the ground or equilibrium state for some values of the pairing interaction and the molecular field. Thermodynamic properties of such gapless superconducting. states are investigated extensively. Special attention is paid on the properties of the phase transitions from such superconducting states to the other states.

The Early Field Defects in Glaucoma

Abstract: the visual field. We cannot rule out glaucoma by testing a predetermined or specific area in the visual field. A complete examination of the visual field is best performed by using both static and kinetic perimetry together. This seems to constitute the best means of modern quantitative perimetry. Scatter of test points can be controlled only by careful attention to numerous details involving physical, pharmacological, physiological, and psychological factors, the \"chaff\" which must be differentiatied from the \"wheat\"—the pathological patterns to be delineated in testing the visual field. The factors causing scatter also influence the reproducibility of a given visual field from one date to another, as do the refractive media, pupil size, mental status, and choice of data points.

A Field Theoretic Model for electron-Nucleon Deep Inelastic Scattering

Abstract: The structure functions for inelastic electron-nucleon scattering are studied in the Bjorken limit in the framework of canonical field theory. The "parton" model of Feynman is derived and the structure functions' asymptotic behavior for large energy transfers is computed.

Time response of the high-field electron distribution function in GaAs

Abstract: Numerical calculations have been made of the high-field electron distribution function for GaAs, its small-signal frequency response and its behavior in large sinusoidal electric fields-The response speed is limited by the low scattering rate within the (000) valley. With increasing frequency the threshold field for negative conductivity rises and the negative mobility and oscillator efficiency fall. The free-electron dielectric constant is positive at high fields, with a peak near the threshold field.

A Programmable Magnetic Field Mass Spectrometer with On-Line Data Processing

Abstract: A single focusing, 30.48 cm radius, 60° sector magnet mass spectrometer was constructed with symmetric conjugate foci calculated from fringe field data and corresponding to a beam deflection of 68°. Experimental and calculated optical characteristics agree well. A rotating coil probe and a rate coil are employed as field sensors for a nulling device and for field scanning. The magnetic field can be set to 27 values corresponding to the center of spectral lines and zero lines on both sides of each peak. The automatic scanning consists of: (1) rapid field change between adjacent field values (~500 G/sec); (2) locking in at the preset field values (~0.3 sec); (3) remaining in a channel for a preset time during which the ion beam current is integrated and the data digitized. Repeated arbitrary excursions between channels do not cause effective field variations of more than |DeltaB/B| = 2×10^–5. For 0.2 mm source and 0.64 mm collector slit settings, a typical peak at mass 88 is flat for 2.7 G to 0.01% at a 14 kV accelerating potential. Data consist of channel intensity, scale factors, and internally provided clock time; data signals drive a typewriter and tape punch. A cyclic scan of five isotopes including background requires 35 sec. A segment of data (~10 cycles) is processed by the computer and the results returned to the operator.

Examples of Momentum Distributions in the Electromagnetic Field and in Matter

Abstract: Momentum conservation and the validity of the center-of-mass law are examined for systems made up of electrostaticcharges and magnets, in terms of the requirements of special relativitytheory. The approach used is that of a quasimicroscopic electromagnetictheory, in which the interaction of the field with material bodies is described by using models for these bodies which involve charge and current densities. It is shown that if small “electromagnetic mass” terms are neglected, both conservation of momentum and the center-of-mass law hold in all cases. In some cases a “hidden momentum” contained in stationary matter plays an important role, as pointed out recently by Shockley and James [W. Shockley and R. P. James, Phys. Rev. Lett. 18, 876 (1967).] In such cases the center-of-mass law can fail in nonrelativistic theory. This is illustrated by the discussion of a special model. Another case in which a “hidden momentum” required by relativitytheory is important is the explanation of the null result of the Trouton-Noble experiment. This is discussed in Sec. V.

Scattering by a Cylindrical Post of Complex Permittivity in a Waveguide

Abstract: An exact solution of the discontinuity problem of a circular cylindrical post of arbitrary complex permittivity centered in a rectangular waveguide with the axis parallel to the electric field vector of the dominant mode has been set up and numerical results based directly on this solution have been found rising an electronic computer. The method used divides the waveguide up into three different regions by introducing two imaginary plane walls perpendicular to the waveguide walls. In the center region, which contains the cylindrical rod, the electromagnetic field is expanded in cylindrical waves and in the outer regions the field is expanded in waveguide modes. By setting up the boundary conditions at all discontinuity surfaces and performing numerical matching of the fields at the two imaginary walls, a system of linear equatious determining the coefficients of reflection, transmission, and absorption of the field due to the cylindrical rod is found. The structure which is of most interest in the case of a plasma column is a coaxial structure consisting of an inner dielectric cylinder with complex permittivity (the plasma) surrounded by a dielectric sleeve with real, positive permittivity (the glass tube). The theory is therefore developed to apply generally for such structures. From the numerical results, curves have been obtained showing the relationship between the coefficients of reflection and transmission and the (complex) permittivity of the rod material. Such curves maybe used for deducing the microwave properties of a cylindrical rod from measurements of the reflection and transmission coefficient of the rod.

Alternative‐Current Field‐Induced Forces and Their Biological Implications

Abstract: Steady‐state, field‐induced forces on particles of microscopic size become significant at field strength values of the order of 100 v/cm. They include "pearl‐chain formation," i.e. the alignment of particles in the direction of the imposed field, and the orientation of nonspherical particles. The time constant, which describes the speed of these phenomena, depends on field strength, and particle and other parameters. For pulsed fields, a lower level of applied average power can suffice to evoke the phenomena mentioned. Biological implications include the possibility of nonthermal effects of biological significance.

Spontaneous Polarization Measurements in Several Ferroelectric Oxides Using a Pulsed‐Field Method

Abstract: The room‐temperature spontaneous polarizations in LiNbO3, LiTaO3, Ba2NaNb5O15, Sr0.5Ba0.5Nb2O6, Ba1.1Sr0.9NaNb5O15, and Sr2KNb5O15 have been measured directly by a pulsed field method using an aqueous solution of LiCl as the electrode material. The experimental results are: P8 (LiNbO3) = 0.71±0.02 C/m2, P8 (LiTaO3) = 0.50±0.01 C/m2, P8 (Ba2NaNb5O15) = 0.40±0.01 C/m2, P8 (Ba1.1Sr0.9NaNb5O15) = 0.36±0.01 C/m2, P8 (Sr2KNb5O15) = 0.25±0.01 C/m2, and P8 (Sr0.5Ba0.5Nb2O6) = 0.25±0.01 C/m2. Experimental techniques are presented, and the advantages of the pulsed‐field method over hysteresis‐loop methods are discussed.