Structure and correlations for harmonically confined charges

Abstract

Coulomb charges confined by a harmonic potential display a rich structure at strong coupling, both classical and quantum. A simple density functional theory is reviewed showing the essential role of correlations in forming shell structure and order within the shells. An overview of previous comparisons with molecular dynamics and Monte Carlo simulations is summarized and extended. It is shown that correlations for the fluid phase (shell structure only) are well approximated by those for the uniform one-component plasma even at very strong coupling. A corresponding representation of the correlations for the ordered phase is still an open question. The confirmed success for the classical density functional theory is important for the subsequent representation of the quantum case. Here, a mapping of the quantum description onto an equivalent classical description with effective potentials allows direct application of the classical methods, both theory and simulation. This is particularly relevant at low but finite temperatures where quantum simulation methods are compromised. The special case of Coulomb charges in a harmonic trap is the simplest example of more complex systems of experimental interest where confinement and strong coupling play an essential role (e.g., quantum dots, ions in complex traps, electrons on a helium surface, dusty Yukawa plasmas, ultracold neutral plasmas).