The Thomas-Fermi and the Thomas-Fermi-Dirac Models in Two-Dimension- the Effect of Strong Quantizing Magnetic Field

Using Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) models, we have investigated the properties of electron gas inside two-dimensional (2D) Wigner-Seitz (WS) cells in presence of a strong orthogonal quantizing magnetic field. The electron-electron Coulomb exchange interaction in quasi-2D case is obtained. The exact form of exchange term in 2D is derived making the width of the system tending to zero. Further, using the exchange term, the Thomas-Fermi-Dirac equation in 2D is established. It has been observed that only the ionized WS cell can have finite radius in the Thomas-Fermi model, even in presence of a strong quantizing magnetic field. On the other hand, in the Thomas-Fermi-Dirac model a neutral WS cell can have finite radius.Comment: 9 pages LATEX file with two .eps figures (included), some version will appear in EPJ D 71:5 (2017), DOI: 10.1140/epjd/e2016-70295-

The Study of Two-dimensional Polytropic Stars

In this article we have studied the structure of hypothetical two-dimensional polytropic stars. Considering some academic interest, we have developed a formalism to investigate some of the gross properties of such stellar objects. However, we strongly believe that the formalism developed here may be prescribed as class problem for post-graduate level students in physics or a post-graduate dissertation project work in physics.Comment: 4 pages LATEX file, No Figure, To appear in "The Scientific Voyage Journal