Classical evolution in quantum systems

TL;DR

This paper develops a rigorous framework to distinguish classical and quantum effects in the evolution of quantum systems, connecting classical dynamics with quantum behavior and applying it to various physical phenomena.

Contribution

It derives equations of motion for classical propagation within quantum systems, enabling identification of quantum effects and linking classical laws like Newton's to quantum dynamics.

Findings

Newton's second law emerges from the framework

Applied to nonlinear optics and entanglement dynamics

Provides a method to distinguish quantum effects from static features

Abstract

We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first place. For this reason, we derive from first principles equations of motions that describe the classical propagation in quantum systems. A comparison of this classical model with the actual temporal quantum behavior enables us to identify quantum phenomena in the system's dynamics and distinguish them from static quantum features at individual points in time. For instance, we show how Newton's second law emerges as a special case of our general treatment, connecting it to a Schr\"odinger-type equation. As applications of our universal technique, we analyze nonlinear optical processes, semiclassical models, and the multipartite entanglement dynamics of macroscopic ensembles.