Dynamical screening of the Coulomb interaction for two confined electrons in a magnetic field
Abstract
We show that a difference in time scales of vertical and lateral dynamics permits one to analyze the problem of interacting electrons confined in an axially symmetric three-dimensional potential with a lateral oscillator confinement by means of the effective two-dimensional Hamiltonian with a screened Coulomb interaction. Using an adiabatic approximation based on action-angle variables, we present solutions for the effective charge of the Coulomb interaction (screening) for a vertical confinement potential simulated by parabolic, square, and triangular wells. While for the parabolic potential the solution for the effective charge is given in a closed anlytical form, for the other cases similar solutions can be easily calculated numerically.
Keywords
Cite
@article{arxiv.0809.4285,
title = {Dynamical screening of the Coulomb interaction for two confined electrons in a magnetic field},
author = {N. S. Simonovic and R. G. Nazmitdinov},
journal= {arXiv preprint arXiv:0809.4285},
year = {2008}
}
Comments
10 pages, 6 figures