Correlation energy of an electron gas: a functional approach

Correlation effects of an electron gas in an external potential are derived using an Effective Action functional method. Corrections beyond the random phase approximation (RPA) are naturally incorporated by this method. The Effective Action functional is made to depend explicitly on two-point correlation functions. The calculation is carried out at imaginary time. For a homogeneous electron gas, we calculate the effect of exchange on the ring diagrams at zero temperature and show how to include some of the ladder diagrams. Our results agree well with known numerical calculations. We conclude by showing that this method is in fact a variant of the time dependent density functional method and suggest that it is suitable to be applied to the study of correlation effects in the non-homogeneous case.Comment: 20 figures numbered as in the tex

An Accurate Kinetic Scheme for 3D Solution of the Boltzmann Equation

Low speed neutral particle transport, in long mean free path (LMFP) environments, presents challenges for well‐established techniques, such as the direct simulation Monte Carlo (DSMC) method. In particular, at low flow velocities, statistical methods suffer from noise that may render them impractical in LMFP environments [1]. We describe a non‐statistical (no random numbers are used) kinetic model for particle transport [2, 3, 4]. The behavior of particles is handled in two stages, Ballistic and Collisional. The ballistic operator tracks the location of the particles across a phase space mesh until the particles undergo a collision. The collision operator redistributes the particles in direction and energy in such a way as to conserve momentum and energy at each spatial location of the phase space mesh. In the past, the method has been applied to heat transport in LMFP environments [4]. The current application centers on flow past a micro air foil. We focus on the method and its extension to handle directional flows. Some typical results for high Knudsen number, (Kn  =  )(Kn=λL), flows past a flat plate are presented. © 2003 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87927/2/59_1.pd