Classicality of a quantum oscillator

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

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. By using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find failures of consistency of the dynamics of hybrid classical-quantum systems from both perspectives. 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 nonconservation of energy in the quantum system. By 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. We estimate the timescale for these violations, which is generically rather short. 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.

Original languageEnglish
Article number032122
Pages (from-to)1-8
Number of pages8
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number3
Publication statusPublished - 16 Mar 2016


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