Microscopic stress tensors in quantum systems

Abstract

Microscopic stress tensors are derived for the local-density-approximation and Hartree-Fock models for quantum systems. Dynamically derived stress tensors appear as elements of a continuity equation for the force density in direct correspondence to Newton's laws of classical physics. Equilibrium stress tensors S, derived from the dynamics of the model satisfy a simple, microscopic relationship, divS=0, balancing electric field and momentum-flux contributions at each point in a quantum system. Stress tensors are well-behaved, integrable functions of position which tend to zero as ${r}^{\mathrm{\ensuremath{-}}4}$ at large distances r from finite Coulombic systems. The microscopic stress tensor and pressure are shown to be consistent with macroscopic expressions for these quantities. Comparisons are made of the present work to related work on microscopic stress.