Symplectic geometry and Koopman dynamics at the quantum-classical interface

TL;DR

This paper explores the intersection of symplectic geometry and Koopman dynamics to address the complex interaction between quantum and classical systems, offering a novel mathematical framework for understanding their interface.

Contribution

It introduces a new approach combining symplectic geometry with Koopman theory to analyze quantum-classical interactions, advancing theoretical understanding.

Findings

Provides a unified geometric framework for quantum-classical interactions

Demonstrates potential for new insights into quantum measurement processes

Lays groundwork for future research in quantum-classical hybrid systems

Abstract

Going back to the early days in the history of quantum mechanics, the interaction of quantum and classical systems stands among the most intriguing open questions in science and makes its appearance in several fields, from physics to chemistry. Recently, a new perspective on this problem was unfolded by an unprecedented combination of symplectic geometry and Koopman's formulation of classical mechanics.