Hybrid quantum-classical models as constrained quantum systems

TL;DR

This paper develops a formalism for hybrid quantum-classical systems using constrained Hamiltonian dynamics, revealing properties that differ from purely quantum or classical systems.

Contribution

It introduces a new Hamiltonian-based framework for hybrid systems, enabling consistent dynamics and highlighting unique properties of such systems.

Findings

Derived hybrid dynamical equations from constrained Hamiltonian systems.

Showed hybrid systems possess properties beyond classical and quantum systems.

Provided a formalism that can be used to analyze hybrid quantum-classical interactions.

Abstract

Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions for classical behavior are imposed on one of its subsystems and the corresponding hybrid dynamical equations are derived. The presented formalism suggests that the hybrid systems have properties that are not exhausted by those of quantum and classical systems.