Physics – Mathematical Physics
Scientific paper
2009-03-12
J. Phys. A 43, 255204 (2010)
Physics
Mathematical Physics
LaTeX, 34 pp., 12 figures; final version (v5) to be published in J. Phys. A. This version contains only the part of the previo
Scientific paper
We investigate the particle and kinetic-energy densities for a system of $N$ fermions confined in a potential $V(\bfr)$. 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 $\bfr$, 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 $N$, we show that they practically are surprisingly accurate also for moderate values of $N$.
Brack Matthias
Koch Alan
Murthy M. V. N.
Roccia Jerôme
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