How classical is a quantum oscillator?

Aida Ahmadzadegan, Robert B. Mann, Daniel R. Terno

Published 2015-10-14Version 1

Gaussian quantum systems capture many important quantum features, but can be simulated classically. Using both the Koopmanian and phase-space formalisms we investigate how robust this classicality is. We find from both perspectives that failures of consistency of the dynamics of a hybrid classical-quantum system are exhibited. By demanding that no unobservable operators couple to the quantum sector in the Koopmanian formalism, we show that the classical equations of motion act on their quantum counterparts without experiencing any back-reaction, resulting in non-conservation of energy in the quantum system. Using the phase-space formalism we study the short time evolution of the moment equations of a hybrid classical-Gaussian quantum system, and observe violations of the Heisenberg Uncertainty Relation in the quantum sector for a broad range of initial conditions. This inconsistency indicates that while many explicitly quantum effects can be represented classically, quantum aspects of the system cannot be fully masked. We comment on the implications of our results for quantum gravity.