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- W3105012189 abstract "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 $N$." @default.
- W3105012189 created "2020-11-23" @default.
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- W3105012189 date "2010-05-27" @default.
- W3105012189 modified "2023-09-25" @default.
- W3105012189 title "Exact and asymptotic local virial theorems for finite fermionic systems" @default.
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- W3105012189 doi "https://doi.org/10.1088/1751-8113/43/25/255204" @default.
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