Classicality of a quantum oscillator
arXiv:1510.04112 · doi:10.1103/PhysRevA.93.032122
Abstract
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. 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 a 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 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. We estimate the time scale 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.
References in corpus (3)
Cited by in corpus (10)
- Witnessing non-classicality beyond quantum theory
- Spin and localization of relativistic fermions and uncertainty relations
- Canonical bracket in quantum-classical hybrid systems
- Gravitational interaction through a feedback mechanism
- Emergent dark energy via decoherence in quantum interactions
- Vindication of entanglement-based witnesses of non-classicality in hybrid systems
- Phase space quantum-classical hybrid model
- Classical Propagation in the Quantum Inverted Oscillator
- Gravity as a classical channel and its dissipative generalization
- Covariant operator bases for continuous variables