A Geometric Formulation of Quantum Stress Fields

Details A Geometric Formulation of Quantum Stress Fields A Geometric Formulation of Quantum Stress Fields

2001-12-03

arxiv.org/abs/cond-mat/0112041v1

Physics

Condensed Matter

Materials Science

22 pages, 2 figures. Submitted to Physical Review B. This paper supersedes cond-mat/0006274

Scientific paper

10.1103/PhysRevB.65.224117

We present a derivation of the stress field for an interacting quantum system within the framework of local density functional theory. The formulation is geometric in nature and exploits the relationship between the strain tensor field and Riemannian metric tensor field. Within this formulation, we demonstrate that the stress field is unique up to a single ambiguous parameter. The ambiguity is due to the non-unique dependence of the kinetic energy on the metric tensor. To illustrate this formalism, we compute the pressure field for two phases of solid molecular hydrogen. Furthermore, we demonstrate that qualitative results obtained by interpreting the hydrogen pressure field are not influenced by the presence of the kinetic ambiguity.

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