A one dimensional microscopical model for the study of the coherence in the stopping power problem. Part 2

Abstract

A frictional quantum mechanical system consisting of a particle being scattered inelastically by a chain ofN infinitely heavy, equidistantly spaced two-level atoms is studied. In continuation of Part 1 of this work (G. Süßmann, P. Szilas, Z. Phys. B-Condensed Matter39, 125 (1980)) where the stationary problem has been considered the time dependent problem of a Gaussian wave packet impinging on the target atoms is treated. The reduced density matrix 〈x′|ρ _R (t)|x″〉 of the particle is calculated. With this explicit expression the time derivative of the mean positiond<x>/dt is found in agreement with the stationary mean velocity$\bar \upsilon (x)$ of Part 1. As a measure of the incoherence of ρ _R , i.e. the deviation of the state of the particle from a pure state, the quantityI:=1-Tr(ρ ² _R ) is calculated for the quasi elastic case, and an estimate is given for the inelastic case.