DECAY PROPERTIES OF THE FINITE-TEMPERATURE DENSITY MATRIX IN METALS

Using ordinary Fourier analysis, the asymptotic decay behavior of the density matrix ${F(r,r}^{\ensuremath{'}})$ is derived for the case of a metal at a finite electronic temperature. An oscillatory behavior that is damped exponentially with increasing distance between $r$ and ${r}^{\ensuremath{'}}$ is found. The decay rate is not only determined by the electronic temperature, but also by the Fermi energy. The theoretical predictions are confirmed by numerical simulations.