Investigation of the Dynamic Properties of the Electron Gas by Quasi-Classical Simulations

Abstract

The electron gas on a uniform positive background is an important theoretical model. Both the interactions due to Coulomb forces (i.e, the coupling) and quantum statistical effects due to the Fermi character (i.e., the degeneracy) determine the properties of the electron plasma. To characterize the degeneracy of the electron system the dimensionless parameter is introduced, where T is the temperature (in energy units), n the electron density and is the Fermi energy. Further we define the coupling constant as a being the Wigner–Seitz radius. Important characteristics of the electron gas are the dielectric function and the dynamic structure factor. Knowing these functions the plasma dispersion relation, static correlation functions, and thermodynamic potentials of the electron gas can be obtained. In order to check the validity of the different analytical approaches for the calculation of the dielectric function of a coupled electron gas microscopic simulations of the quantum electron gas could be very useful. Classical simulations of the one component plasma were already performed by Hansen et al. In this paper the dynamic properties of the quantum electron gas will be investigated on the basis of quasi-classical molecular dynamics simulations. In order to treat the quantum electron gas by quasi-classical simulations we make use of effective pair potentials. An effective potential depending only on the space coordinates leads necessarily to the Maxwell momentum distribution. Since we want to model the momentum distribution of an electron gas governed by Fermi statistics we have to include in our simulations momentum-dependent interaction terms. Our approach follows a line developed by a series of authors as e.g., Wilets and Kirschbaum, Dorso et al.,. We mention here also the wave packet dynamics approach as an alternative possibility to model the electron gas by quasiclassical simulations, In our model we approximate the real quantum dynamics of the electron system by a phase space dynamics of Hamilton type with certain constraints given by the effective