The mean field approximation and disentanglement

TL;DR

This paper introduces a nonlinear modification to the Schrödinger equation that suppresses entanglement without altering product state evolution, with significant effects observed in a two-spin system under specific conditions.

Contribution

It proposes a new nonlinear term in the Schrödinger equation that reduces entanglement while preserving unitarity, and analyzes its effects on a two-spin system.

Findings

The added nonlinear term suppresses entanglement in quantum systems.

The modified dynamics significantly affect two-spin systems near the Hartmann Hahn matching condition.

The nonlinear term does not impact the evolution of product states.

Abstract

The mean field approximation becomes applicable when entanglement is sufficiently weak. We explore a nonlinear term that can be added to the Schr\"{o}dinger equation without violating unitarity of the time evolution. We find that the added term suppresses entanglement, without affecting the evolution of any product state. The dynamics generated by the modified Schr\"{o}dinger equation is explored for the case of a two-spin 1/2 system. We find that for this example the added term strongly affects the dynamics when the Hartmann Hahn matching condition is nearly satisfied.