Fredholm Approximations in the Scalar Bethe-Salpeter Equation

1974 ◽  
Vol 29 (6) ◽  
pp. 916-923
Author(s):  
W. Bauhoff
Keyword(s):  
Angular Momentum ◽  
Variational Methods ◽  
Vertex Function ◽  
Feynman Parameter ◽  
Special Cases

The Fredholm approximation is discussed in the framework of the scalar Bethe-Salpeter equation. The trace of the angular momentum decomposed kernel is expressed in terms of Feynman parameter integrals which shows the relation to the vertex function. A new derivation for this representation is given which is far more direct than the previous one. Using this representation, several general features of the eigenvalues are discussed. For special cases, the trace is computed explicitly, and the numerical values are compared with the exact ones, obtained by variational methods.

scholarly journals Observations of Binaries and Evolutionary Implications

1984 ◽  
Vol 80 ◽  
pp. 199-227
Author(s):  
C. De Loore
Keyword(s):  
Mass Transfer ◽  
Angular Momentum ◽  
Mass Transfer Process ◽  
Transfer Phase ◽  
X Ray ◽  
Special Cases ◽  
Angular Momentum Loss ◽  
Spectral Ranges ◽  
X Ray Binaries

AbstractComparison of the characteristics of groups of stars in various evolutionary phases and the study of individual systems allow to make estimates of the parameters governing mass loss and mass transfer. Observations enable us in a few cases to determine geometric models for binaries during or after the mass transfer phase (disks, rings, common envelopes, symbiotics, interacting binaries, compact components).From spectra taken at different phases, radial velocity curves can be derived and masses and radii can be determined. In special cases spectra in different spectral ranges (visual, UV, X-ray) are required for the determination of the radial velocities of the two components (for X-ray binaries, for systems with hot and cool components). Information on parameters related to the mass transfer process enables us to consider non conservative evolution - i.e. the computation of evolutionary sequences with the assumption that mass and angular momentum not only are transferred from one of the components towards the other one, but that also mass and angular momentum can leave the system. Careful and detailed analysis of the observations allows in certain cases to determine the parameters governing this mass and angular momentum loss, and for contact phases, to determine the degree of contact.

scholarly journals Verallgemeinerte Boltzmann-Gleichung für mehratomige Gase

1967 ◽  
Vol 22 (12) ◽  
pp. 1871-1889 ◽  
Author(s):  
S. Hess
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Boltzmann Equation ◽  
Transport Equation ◽  
Internal State ◽  
Quantum Mechanical ◽  
Collision Term ◽  
Special Cases ◽  
Generalized Boltzmann Equation ◽  
Non Local

A generalized quantum mechanical Boltzmann equation is derived for the one particle distribution operator of a dilute gas consisting of molecules with arbitrary internal degrees of freedom. The effect of an external, time-independent potential on the scattering process is taken into account. The collision term of the transport equation contains the two-particle scattering operator T and its adjoint in a bilinear way and is non-local. The conservation equations for number of particles, energy, momentum and angular momentum as well as the H-theorem are deduced from the transport equation. One obtains the correct equilibrium distribution operator even in the presence of an external field (e. g. for particles with spin in a homogeneous magnetic field). Some special cases of the generalized Boltzmann equation are discussed treating position and momentum of a particle as classical variables but characterizing the internal state of a molecule by quantum mechanical observables. Using the local part of the collision term only and considering molecules with degenerate, but sufficiently separated internal energy levels one arrives at the Waldmann-Snider equation, which in turn comprises the Waldmann equation for particles with spin and the Wang Chang-Uhlenbeck equation. Special attention is drawn to the case of particles with spin in a magnetic field. Finally, for particles with spin, the local conservation equation for angular momentum, i.e. the Barnett effect (magnetization by rotation) and the antisymmetric part of the pressure tensor are derived from the generalized Boltzmann equation with non-local collision term.

The Foucault pendulum viewed as a spherical pendulum placed in a rotating reference system

2016 ◽  
Vol 94 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Miguel de Icaza-Herrera ◽  
Víctor Manuel Castaño
Keyword(s):  
Angular Momentum ◽  
Angular Velocity ◽  
Boundary Conditions ◽  
Reference System ◽  
Mechanical Energy ◽  
Angular Distance ◽  
Spherical Pendulum ◽  
Foucault Pendulum ◽  
The Earth ◽  
Special Cases

For a pendulum of a given length, installed at any fixed latitude, the motion depends on three variables: the total mechanical energy, connected with the maximum angular distance of the bob from the vertical; the projection of the angular momentum along the vertical, connected with the shape of its orbit along the surface of a sphere, which may be described as a veering ellipse recalling the orbit of Mercury; and the angular velocity, Ω, of the rotating reference system given by that of the Earth. When the value of one of these variables is negligible, the ensuing motion has already been calculated in analytical grounds: a plummet, a Foucault pendulum, or a spherical pendulum including as a special case the so-called plane pendulum. This paper offers a Lagrangian approach in the case when Ω is the sidereal angular velocity of the Earth. To our knowledge, these are the first analytical solutions for any boundary conditions. When the boundary conditions are such that the bob passes through the vertical (i.e., the direction defined by the plummet), the behavior of the pendulum is as expected: the veering velocity of the plane equals the angular velocity of the Earth times the sine of the latitude. This state is reached when the projection of its angular momentum along the vertical vanishes. However, if that projection takes any other value, the motion is produced along a veering ellipse and the time rate of advance of the major axis is the sum of the previous result plus the spherical pendulum contribution. Our solutions include, as special cases, those of the spherical pendulum, or the ideal Foucault pendulum with finite amplitude.

scholarly journals Observable Effects of Rotation on Stellar Abundances

1993 ◽  
Vol 137 ◽  
pp. 333-346
Author(s):  
Suchitra Balachandran
Keyword(s):  
Angular Momentum ◽  
Main Sequence ◽  
Meridional Circulation ◽  
Theoretical Models ◽  
Stellar Abundances ◽  
Stellar Interior ◽  
Special Cases ◽  
Abundance Anomalies ◽  
Effects Of Rotation

AbstractThis is a review of our understanding of the effects of rotation on the stellar interior through an examination of observed surface stellar abundances. First, the evolution of angular momentum from the pre-main sequence through the giant phase is summarized. Attempts are then made to decipher the signature of abundance anomalies due to meridional circulation and rotational braking with reference to available theoretical models. Finally, special cases such as tidally-locked binaries and chromospherically-active giants are examined to determine if their rotational peculiarites have induced abundance anomalies.

Dirac Spin and Angular Momentum of the Stationary Axisymmetric Space-Time in the Teleparallel Gravity

2020 ◽  
Author(s):  
M F Mourad
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Axial Vector ◽  
Teleparallel Gravity ◽  
Space Time ◽  
Special Cases ◽  
Vector Part ◽  
Dirac Spin

In the framework of teleparallel equivalent to general relativity, the stationary axisymmetric space-time in the teleparallel gravity for two different sets of tetrad fields have been investigated. For these sets, we have obtained the expressions for the torsion vector, torsion axial-vector and the angular momentum of the solution. We found that the obtained expressions of the torsion axial-vector and the angular momentum are, in general quite different in both two sets of tetrad fields, while the expressions for the torsion vector have the same value. Moreover, the vector part connected with Dirac spin has been evaluated as well. Finally, special cases of the stationary axisymmetric space-time are discussed.

scholarly journals THEOREM OF CHANGE IN THE ANGULAR MOMENTUM OF A SYSTEM WITH RESPECT TO A MOVING CENTER

1987 ◽  
Vol 9 (1) ◽  
pp. 26-32
Author(s):  
Nguyen Dang To
Keyword(s):  
Differential Equation ◽  
Angular Momentum ◽  
Rigid Body ◽  
Center Of Mass ◽  
Plane Motion ◽  
Absolute Motion ◽  
Special Cases ◽  
Fixed Center

The Literatures of theorical mechanics only present, the theorem of change in the angular momentum of a system with respect to a fixed center; with respect to the center of mass ... In this paper we developed that theorem With respect to any moving center in relative and absolute motion of system. Having applied this theorem in many special cases of plane motion of a rigid body; we can write directly the differential equation without reactions that describes the rotation of that body so as its integration will be more convenient.

Mach’s principle and the structure of dynamical theories

1982 ◽  
Vol 382 (1783) ◽  
pp. 295-306 ◽  
Keyword(s):  
Field Theory ◽  
Angular Momentum ◽  
Formal Structure ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Newtonian Dynamics ◽  
Special Cases ◽  
General Dynamics ◽  
Entire Universe ◽  
The Universe

A structure of dynamical theories is proposed that implements Mach’s ideas by being relational in its treatment of both motion and time. The resulting general dynamics, which is called intrinsic dynamics and by construction treats the evolution of the entire Universe, is shown to admit as special cases Newtonian dynamics and Lorentz-invariant field theory provided the angular momentum of the Universe is zero in the frame in which its momentum is zero. The formal structure of Einstein’s general theory of relativity also fits the pattern of intrinsic dynamics and is Machian according to the criteria of this paper provided the so-called thin-sandwich conjecture is generically correct.

Generalized Schwinger boson realizations and the oscillator-like coherent states of the rotation groups and the asymmetric top

1979 ◽  
Vol 57 (7) ◽  
pp. 998-1021 ◽  
Author(s):  
P. Gulshani
Keyword(s):  
Angular Momentum ◽  
Coherent States ◽  
Euler Angles ◽  
Boson Realization ◽  
Special Cases ◽  
Asymmetric Top ◽  
Rotation Groups ◽  
Angular Momentum Algebra

Various definitions of the coherent states of the angular momentum are shown to be special cases of the oscillator-like coherent states of the groups SU(2) and SO(3) obtained by Mikhailov on the basis of a generalized Schwinger boson realization of the angular momentum algebra. This realization is then generalized to that of the angular momentum algebra of an asymmetric top by means of a transformation from the Euler angles to the Cayley–Klein parameters. The oscillator-like coherent states of an asymmetric top, analogous to those of Mikhailov, are then constructed. It is, then, shown that Janssen's and Mostowski's definitions of the coherent states of a top are special cases of these.

scholarly journals Spin angular momentum density in the tight focus of a light field with phase and polarization singularities

2019 ◽  
Vol 43 (6) ◽  
pp. 1098-1102
Author(s):  
A.A. Kovalev ◽  
V.V. Kotlyar ◽  
D.S. Kalinkina
Keyword(s):  
Angular Momentum ◽  
Light Field ◽  
Bessel Beam ◽  
Momentum Density ◽  
Transverse Component ◽  
Optical Vortices ◽  
Spin Angular Momentum ◽  
Special Cases ◽  
Order Of Magnitude ◽  
Aplanatic System

For a light field with both phase and polarization singularities at its center, expressions are obtained that describe the distribution of the spin angular momentum (SAM) density in the sharp focal spot of an aplanatic system. These expressions include the radial, azimuthal, and longitudinal SAM components. As special cases, focusing of optical vortices with radial, azimuthal, and saddle polarizations is studied. Using the Bessel beam as an example, it is shown that in some areas in the focal plane the longitudinal SAM component is zero (resulting in a photonic wheel), while in others it is an order of magnitude less than the transverse component.

Electron Beam Damage of Biomolecules Assessed by Energy Loss Spectroscopy

1978 ◽  
Vol 36 (3) ◽  
pp. 61-69
Author(s):  
M. Isaacson ◽  
M.L. Collins ◽  
M. Listvan
Keyword(s):  
Electron Microscopy ◽  
Radiation Damage ◽  
Structural Integrity ◽  
Analytical Electron Microscopy ◽  
High Dose ◽  
Dose Rates ◽  
Special Cases ◽  
Analytical Electron ◽  
Atom Migration ◽  
Beam Damage

Over the past five years it has become evident that radiation damage provides the fundamental limit to the study of blomolecular structure by electron microscopy. In some special cases structural determinations at very low doses can be achieved through superposition techniques to study periodic (Unwin & Henderson, 1975) and nonperiodic (Saxton & Frank, 1977) specimens. In addition, protection methods such as glucose embedding (Unwin & Henderson, 1975) and maintenance of specimen hydration at low temperatures (Taylor & Glaeser, 1976) have also shown promise. Despite these successes, the basic nature of radiation damage in the electron microscope is far from clear. In general we cannot predict exactly how different structures will behave during electron Irradiation at high dose rates. Moreover, with the rapid rise of analytical electron microscopy over the last few years, nvicroscopists are becoming concerned with questions of compositional as well as structural integrity. It is important to measure changes in elemental composition arising from atom migration in or loss from the specimen as a result of electron bombardment.

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