Equivalence of Two Approaches for Quantum-Classical Hybrid Systems

TL;DR

This paper proves the equivalence of mean-field theory and hybrid brackets approach in describing quantum-classical hybrid systems, clarifying their relationship and providing a unified framework.

Contribution

It establishes the theoretical equivalence between two commonly used methods for quantum-classical hybrid systems, enhancing understanding and consistency.

Findings

Mean-field theory and hybrid brackets are mathematically equivalent.

The equivalence provides a unified description of quantum-classical hybrids.

This result clarifies the relationship between two prevalent approaches.

Abstract

We discuss two approaches that are used frequently to describe quantum-classical hybrid system. One is the well-known mean-field theory and the other adopts a set of hybrid brackets which is a mixture of quantum commutators and classical Poisson brackets. We prove that these two approaches are equivalent.