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Advances in Condensed Matter Physics
Volume 2015 (2015), Article ID 851356, 4 pages
Research Article

Shape-Dependent Energy of an Elliptical Jellium Background

Department of Physics, Prairie View A&M University, Prairie View, TX 77446, USA

Received 7 April 2015; Accepted 27 April 2015

Academic Editor: Sergei Sergeenkov

Copyright © 2015 Orion Ciftja et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The jellium model is commonly used in condensed matter physics to study the properties of a two-dimensional electron gas system. Within this approximation, one assumes that electrons move in the presence of a neutralizing background consisting of uniformly spread positive charge. When properties of bulk systems (of infinite size) are studied, shape of the jellium domain is irrelevant. However, the same cannot be said when one is dealing with finite systems of electrons confined in a finite two-dimensional region of space. In such a case, geometry and shape of the jellium background play a role on the overall properties of the system. In this work, we assume that the region where the electrons are confined is represented by a jellium background charge with an elliptical shape. It is shown that, in this case, the Coulomb self-energy of the elliptically shaped region can be exactly calculated in closed analytical form by using suitable mathematical transformations. The results obtained reveal the external influence of geometry/shape on the properties of two-dimensional systems of few electrons confined to a small finite region of space.