Exact and asymptotic local virial theorems for finite fermionic systems
Abstract
We investigate the particle and kinetic-energy densities for a system of fermions confined in a potential . In an earlier paper [J. Phys. A: Math. Gen. {\bf 36}, 1111 (2003)], some exact and asymptotic relations involving the particle density and the kinetic-energy density locally, i.e. at any given point , were derived for isotropic harmonic oscillators in arbitrary dimensions. In this paper we show that these {\it local virial theorems} (LVT) also hold exactly for linear potentials in arbitrary dimensions and for the one-dimensional box. We also investigate the validity of these LVTs when they are applied to arbitrary smooth potentials. We formulate generalized LVTs that are supported by a semiclassical theory which relates the density oscillations to the closed non-periodic orbits of the classical system. We test the validity of these generalized theorems numerically for various local potentials. Although they formally are only valid asymptotically for large particle numbers , we show that they practically are surprisingly accurate also for moderate values of .
Cite
@article{arxiv.0903.2172,
title = {Exact and asymptotic local virial theorems for finite fermionic systems},
author = {M. Brack and A. Koch and M. V. N. Murthy and J. Roccia},
journal= {arXiv preprint arXiv:0903.2172},
year = {2015}
}
Comments
LaTeX, 34 pp., 12 figures; final version (v5) to be published in J. Phys. A. This version contains only the part of the previous version (v3) on local virial theorems; the semiclassical theory has appeared as arXiv:0912.4374v1 [math-ph] and is published in Phys. Rev. E 81, 011118 (2010)