We study characteristic schemes for a model problem for the Fermi pencil beam equation. The objective is twofold: (i) To design eecient and accurate numerical schemes based on the principle of solving a particle transport problem, exactly, on each collision free spatial segment combined with a projection on each collision site, from a pre collision angle and energy coordinates (AE) to a post co...

A kinetic equation which combines the quasiparticle drift of Landau’s equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider’s equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections. The medium effects on binary coll...

We consider a Fermi pencil beam model in two space dimensions (x; y), where x is aligned with the beam's penetration direction and y together with the scaled angular variable z, correspond to a bounded symmetric , transversal cross section. We study some fully discrete numerical schemes using the standard Galerkin and streamline diiusion nite element methods for discretization of the transversa...

The recently derived nonlocal quantum kinetic equation for dense interacting Fermi systems combines time derivatives with finite time stepping known from the logistic mapping. This continuous delay differential equation is a consequence of the microscopic delay time representing the dynamics of the deterministic chaotic system. The responsible delay time is explicitly calculated and discussed f...

Using Thomas-Fermi-Dirac equation within the exchange-correlation scheme and a Z-dependent trial solution, the ground state binding energy for neutral, positively, and negatively charged atoms are calculated. Comparing to the results obtained in earlier works, the values of the binding energy estimated here for both light and heavy atoms agree nicely with the Hartree-Fock values. We have also c...

In this paper, a newly proposed analytical scheme by the authors namely the improved di erential transform method is employed to provide an explicit series solution to the Thomas Fermi equation. The solution procedure is very straightforward, requiring merely elementary operations together with di erentiation, and ends up in a recursive formula involving the Adomian polynomials to a ord the unk...

The aim of this paper is to introduce a new approximate method, namely the Modified Laplace Padé Decomposition Method (MLPDM) which is a combination of modified Laplace decomposition and Padé approximation to provide an analytical approximate solution to Thomas-Fermi equation. This new iteration approach provides us with a convenient way to approximate solution. A good agreement between the obt...

We study the dynamic response of a one-dimensional double-barrier nanostructure to an ac bias. Combining the Schrödinger equation, Poisson equation and the scattering theory, we calculate the internal potential, charge density, and the ac conductance as well. The results show that the charge distribution is antisymmetric with respect to the center of the double barrier, and depends crucially on...