Force and pressure in many-particle quantum dynamics

TL;DR

This paper explores how classical concepts like force can be adapted to many-particle quantum systems using Ehrenfest's approach, defining boundary operators to describe quantum kinetic forces and interactions.

Contribution

It introduces a novel operator-based method to describe forces in quantum systems, bridging classical intuition and quantum formalism, applicable to density functional theory and simple models.

Findings

Force operators can describe quantum kinetic forces at boundaries.

Interaction effects can be incorporated via boundary operators.

Method demonstrated on simple quantum models.

Abstract

The Newtonian concept of force may be useful in some aspects of the dynamics of many-particle quantum systems such as fissioning nuclei. Following Ehrenfest's method, we show that the quantum kinetic force between parts of an extended quantum system can be described by an operator acting on the boundary between the two subsystems. The contribution to the force due to a short-ranged particle interaction can also be treated in the same way. This includes interaction effects treated in density functional theory by local functionals. The force operators are applied to several simple models to demonstrate the method.