The Decay Properties of the Finite Temperature Density Matrix in Metals

TL;DR

This paper analyzes how the density matrix in metals decays at finite temperature, revealing oscillatory and exponential damping behavior influenced by temperature and Fermi energy, supported by numerical simulations.

Contribution

It provides a theoretical derivation of the decay properties of the finite temperature density matrix in metals, including the effects of temperature and Fermi energy.

Findings

Density matrix exhibits oscillatory decay damped exponentially

Decay rate depends on electronic temperature and Fermi energy

Numerical simulations confirm theoretical predictions

Abstract

Using ordinary Fourier analysis, the asymptotic decay behavior of the density matrix F(r,r') is derived for the case of a metal at a finite electronic temperature. An oscillatory behavior which is damped exponentially with increasing distance between r and r' 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.