Linear dynamics of quantum-classical hybrids

TL;DR

This paper introduces a linear framework for quantum-classical hybrid dynamics, enabling direct coupling of quantum and classical systems, with potential applications in quantum approximations and foundational studies.

Contribution

It presents a novel linear theory for quantum-classical hybrids that satisfies all consistency requirements, differing from previous nonlinear models.

Findings

Provides a consistent linear hybrid dynamics framework

Extends classical mechanics notions to quantum systems

Potential applications in quantum approximation and foundations

Abstract

A formulation of quantum-classical hybrid dynamics is presented, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. It is of interest for applications in quantum mechanical approximation schemes and may be relevant for the foundations of quantum mechanics, in particular, when it comes to experiments exploring the quantum-classical border. The present linear theory differs from the nonlinear ensemble theory of Hall and Reginatto, but shares with it to fullfill all consistency requirements discussed in the literature, while earlier attempts failed in this respect. Our work is based on the representation of quantum mechanics in the framework of classical analytical mechanics by A. Heslot, showing that notions of states in phase space, observables, Poisson brackets, and related canonical transformations can be naturally extended to quantum mechanics. This is suitably generalized for quantum-classical hybrids here.