Decay properties of the finite-temperature density matrix in metals

Using ordinary Fourier analysis, the asymptotic decay behavior of the density matrix ${F(r,r}^{\prime })$ 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 $r^{\prime }$ 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.