Correlations and sum rules in a half-space for a quantum two-dimensional one-component plasma

Details Correlations and sum rules in a half-space for a quantum two-dimensional one-component plasma Correlations and sum rules in a half-space for a quantum two-dimensional one-component plasma

2007-04-18

arxiv.org/abs/0704.2316v1

J. Stat. Mech. (2007) P05009

Physics

Condensed Matter

Statistical Mechanics

15 pages, to appear in J. Stat. Mech. (JSTAT)

Scientific paper

10.1088/1742-5468/2007/05/P05009

This paper is the continuation of a previous one [L. {\v{S}}amaj and B. Jancovici, 2007 {\it J. Stat. Mech.} P02002]; for a nearly classical quantum fluid in a half-space bounded by a plain plane hard wall (no image forces), we had generalized the Wigner-Kirkwood expansion of the equilibrium statistical quantities in powers of Planck's constant $\hbar$. As a model system for a more detailed study, we consider the quantum two-dimensional one-component plasma: a system of charged particles of one species, interacting through the logarithmic Coulomb potential in two dimensions, in a uniformly charged background of opposite sign, such that the total charge vanishes. The corresponding classical system is exactly solvable in a variety of geometries, including the present one of a half-plane, when $\beta e^2=2$, where $\beta$ is the inverse temperature and $e$ is the charge of a particle: all the classical $n$-body densities are known. For the quantum one-component plasma, two sum rules involving the truncated two-body density (and, for one of them, the density profile) have been derived, a long time ago, by heuristic macroscopic arguments: one sum rule is about the asymptotic form along the wall of the truncated two-body density, the other one is about the dipole moment of the structure factor. In the two-dimensional case at $\beta e^2=2$, we have now explicit expressions up to order $\hbar^2$ of these two quantum densities, thus we can microscopically check the sum rules at this order. The checks are positive, reinforcing the idea that the sum rules are correct.

Affiliated with

Also associated with

No associations

Rating

Correlations and sum rules in a half-space for a quantum two-dimensional one-component plasma does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Correlations and sum rules in a half-space for a quantum two-dimensional one-component plasma, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Correlations and sum rules in a half-space for a quantum two-dimensional one-component plasma will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-405000