Effective nonlinear Ehrenfest hybrid quantum-classical dynamics

TL;DR

This paper investigates the challenges of defining consistent nonlinear Ehrenfest hybrid quantum-classical dynamics, proposing an effective approximation method based on higher-order quantum moments to overcome obstructions in the first quantum moment.

Contribution

It introduces a novel approach to hybrid dynamics by using higher-order quantum moments to address non-linearity issues in Ehrenfest systems.

Findings

Identifies obstructions in defining consistent dynamics for the first quantum moment.

Proposes an effective approximation using a finite number of quantum moments.

Highlights that only a finite number of moments are physically measurable.

Abstract

The definition of a consistent evolution equation for statistical hybrid quantum-classical systems is still an open problem. In this paper we analyze the case of Ehrenfest dynamics on systems defined by a probability density and identify the relations of the non-linearity of the dynamics with the obstructions to define a consistent dynamics for the first quantum moment of the distribution. This first quantum moment represents the physical states as a family of classically-parametrized density matrices $\hat \rho(\xi)$, for $\xi$ a classical point; and it is the most common representation of hybrid systems in the literature. Due to this obstruction, we consider higher order quantum moments, and argue that only a finite number of them are physically measurable. Because of this, we propose an effective solution for the hybrid dynamics problem based on approximating the distribution by those moments and representing the states by them.