Hartree approximation to QCD in the Fock-Schwinger gauge

1987 ◽  
Vol 36 (6) ◽  
pp. 1922-1928 ◽  
Author(s):  
M. Schaden ◽  
St. Glazek ◽  
E. Werner
Keyword(s):  
Hartree Approximation

scholarly journals Calculation of nuclear energies and stability by the statistical method

1940 ◽  
Vol 174 (959) ◽  
pp. 523-545 ◽  
Keyword(s):  
Statistical Theory ◽  
Binding Energy ◽  
Statistical Method ◽  
Atomic Number ◽  
Quantum States ◽  
Hartree Approximation ◽  
Stable Nucleus ◽  
The Stability

Leaving out of consideration those nuclei of small atomic number it is possible to develop a statistical theory of nuclei. Bethe and Bacher (1936, p. 149), as well as many other writers, have treated this subject in great detail starting from the Hartree approximation. All these investigations were mainly concerned with the binding energy, and not much attention has been paid so far to the stability of nuclei according to the statistical theory, except the determination of the most stable nucleus with a given atomic number: this is due to the fact that previous investigators have always neglected to distinguish between quantum states with opposite spin, thereby losing the distinction between “odd” and “even” nuclei, which is essential for stability considerations.

scholarly journals WIGNER–POISSON AND NONLOCAL DRIFT-DIFFUSION MODEL EQUATIONS FOR SEMICONDUCTOR SUPERLATTICES

2005 ◽  
Vol 15 (08) ◽  
pp. 1253-1272 ◽  
Author(s):  
L. L. BONILLA ◽  
R. ESCOBEDO
Keyword(s):  
Numerical Solutions ◽  
Inelastic Collisions ◽  
Diffusion Equations ◽  
Electron Interaction ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Hartree Approximation ◽  
Semiconductor Superlattices ◽  
Sustained Oscillations ◽  
Model Equations

A Wigner–Poisson kinetic equation describing charge transport in doped semiconductor superlattices is proposed. Electrons are assumed to occupy the lowest miniband, exchange of lateral momentum is ignored and the electron–electron interaction is treated in the Hartree approximation. There are elastic collisions with impurities and inelastic collisions with phonons, imperfections, etc. The latter are described by a modified BGK (Bhatnagar–Gross–Krook) collision model that allows for energy dissipation while yielding charge continuity. In the hyperbolic limit, nonlocal drift-diffusion equations are derived systematically from the kinetic Wigner–Poisson–BGK system by means of the Chapman–Enskog method. The nonlocality of the original quantum kinetic model equations implies that the derived drift-diffusion equations contain spatial averages over one or more superlattice periods. Numerical solutions of the latter equations show self-sustained oscillations of the current through a voltage biased superlattice, in agreement with known experiments.

Hartree Approximation

2019 ◽  
Author(s):  
Marek S. Wartak ◽  
Ching-Yao Fong
Keyword(s):  
Hartree Approximation

Optical excitation waves in a molecular crystal

1964 ◽  
Vol 282 (1390) ◽  
pp. 433-445 ◽  
Keyword(s):  
Refractive Index ◽  
Quantum Theory ◽  
Excited States ◽  
Molecular Crystal ◽  
Optical Excitation ◽  
Time Dependent ◽  
Hartree Approximation ◽  
Quasi Particle ◽  
Quantum Theory Of Radiation ◽  
Classical Picture

We have used the quantum theory of radiation, within the time-dependent Hartree approximation, to study exciton states of a van der Waals molecular crystal. The radiation variables are eliminated to give a semi-classical picture of molecular dipoles interacting through a retarded potential, and the solutions of the Hartree equations are closely connected with the quasi-particle excited states in Agranovich’s theory. In the Lorentz-Lorenz approximation the crystal has excited states which correspond to both longitudinal and transverse exciton weaves, and the refractive index behaves classically. The paper concludes with a brief discussion of metallic reflexion by dye crystals.

scholarly journals Nuclear matter with a Bose condensate of dibaryons in a relativistic Hartree approximation

1998 ◽  
Vol 57 (3) ◽  
pp. 1458-1463 ◽  
Author(s):  
Amand Faessler ◽  
A. J. Buchmann ◽  
M. I. Krivoruchenko
Keyword(s):  
Nuclear Matter ◽  
Bose Condensate ◽  
Hartree Approximation
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