Emergence of Non-Markovian Classical-Quantum Dynamics from Decoherence

TL;DR

This paper demonstrates that classical-quantum dynamics can naturally emerge from decohered quantum systems, with non-Markovian effects and specific conditions for classicality, bridging quantum and classical descriptions of gravity.

Contribution

It provides a general derivation showing classical-quantum dynamics as an effective, decoherence-induced phenomenon with explicit criteria for classicality validity.

Findings

Classical-quantum dynamics arise from decohered quantum systems.

The reduced dynamics are generally non-Markovian.

A positivity condition on nonlocal kernels determines classicality validity.

Abstract

The quantum nature of gravity remains experimentally unverified, despite recent proposals to probe it using tabletop experiments such as gravity-mediated entanglement schemes. In parallel, consistent formulations of classical--quantum dynamics have been developed as alternative descriptions of gravity, in which quantum matter interacts with a classical mediator assumed to be fundamentally classical. In this work, we show that classical--quantum dynamics arise generically as an effective description of fully quantum systems under decoherence, providing a bridge between fully quantum and classical--quantum dynamics. We derive the reduced dynamics, which are generically non-Markovian, using an explicit hidden model in which the mediator is coupled to unobserved environmental degrees of freedom. We identify a concrete criterion for when a classical--quantum interpretation is valid: the semi-Wigner operator associated with the mediator sector must remain positive semidefinite, which can be expressed as a positivity condition on nonlocal kernels governing the evolution. In the short-memory limit, the reduced evolution reproduces Markovian classical--quantum dynamics of Oppenheim and collaborators. Our results imply that a classical mediator can arise effectively from decohered quantum dynamics, so that experimental agreement with classical-quantum models does not uniquely determine whether the mediator is fundamentally classical.