Classical-Quantum Hybrid Models

TL;DR

This paper reviews hybrid classical-quantum models that combine classical and quantum descriptions to simulate system evolution, discussing their motivations, requirements, and limitations, especially in reversible dynamics.

Contribution

It provides a comprehensive overview of existing hybrid models, highlighting their development motivations, key requirements, and the challenges faced, particularly in non-relativistic and reversible contexts.

Findings

Hybrid models integrate classical and quantum mechanics for system evolution.

Limitations exist in non-relativistic schemes, especially regarding reversible dynamics.

The paper outlines the development motivations and requirements for such models.

Abstract

Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the motivation for such models, outline the requirements they must satisfy, and provide explanations for their development. Then we review various popular non-relativistic schemes and their associated limitations, with a particular emphasis on reversible dynamics.