Impediments to mixing classical and quantum dynamics

Abstract

The dynamics of systems composed of a classical sector plus a quantum sector is studied. We show that, even in the simplest cases, (i) the existence of a consistent canonical description for such mixed systems is incompatible with very basic requirements related to the time evolution of the two sectors when they are decoupled. (ii) The classical sector cannot inherit quantum fluctuations from the quantum sector. And, (iii) a coupling among the two sectors is incompatible with the requirement of physical positivity of the theory, i.e., there would be positive observables with a non positive expectation value.

RevTex, 21 pages. Title slightly modified and summary section added

References in corpus (1)

• Coupling Classical and Quantum Variables using Continuous Quantum Measurement Theory

Cited by in corpus (56)

• Understanding quantum measurement from the solution of dynamical models
• Is Quantum Gravity Necessary?
• Mapping Variable Ring Polymer Molecular Dynamics: A Path-Integral Based Method for Nonadiabatic Processes
• Linear dynamics of quantum-classical hybrids
• Hybrid classical-quantum dynamics
• Royal Road to Coupling Classical and Quantum Dynamics
• Interacting classical and quantum ensembles
• On two recent proposals for witnessing nonclassical gravity
• Consistent classical and quantum mixed dynamics
• Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity
• Inconsistency of quantum--classical dynamics, and what it implies
• Hybrid classical-quantum formulations ask for hybrid notions
• Koopman wavefunctions and classical-quantum correlation dynamics
• Statistical consistency of quantum-classical hybrids
• Mixing quantum and classical mechanics and uniqueness of Planck's constant
• Statistical moments for classical and quantum dynamics: formalism and generalized uncertainty relations
• The gravity-related decoherence master equation from hybrid dynamics
• A Quantum-Classical Brackets from p-Mechanics
• Objective trajectories in hybrid classical-quantum dynamics
• The constraints of post-quantum classical gravity
• Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation
• Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible
• Four questions for quantum-classical hybrid theory
• Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths
• Nonquantum Gravity
• Quantum-classical interactions and measurement: a consistent description using statistical ensembles on configuration space
• Robust non-adiabatic molecular dynamics for metals and insulators
• Discrete mechanics, time machines and hybrid systems
• A New Quantization Map
• Semiclassical dynamics in the mixed quantum-classical limit
• Proliferation of observables and measurement in quantum-classical hybrids
• Evaluation of the importance of spin-orbit couplings in the nonadiabatic quantum dynamics with quantum fidelity and with its efficient "on-the-fly" ab initio semiclassical approximation
• Quantum-classical hybrid dynamics - a summary
• Canonical bracket in quantum-classical hybrid systems
• Quantum and Classic Brackets
• Half Quantization
• Comment on ``A quantum-classical bracket that satisfies the Jacobi identity'' [J. Chem. Phys. 124, 201104 (2006)]
• Entropy and canonical ensemble of hybrid quantum classical systems
• Is it time to rethink quantum gravity?
• Mirror-induced decoherence in hybrid quantum-classical theory
• Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states
• Classical-quantum limits
• About the computation of finite temperatureensemble averages of hybrid quantum-classicalsystems with Molecular Dynamics
• Phase space quantum-classical hybrid model
• Separation of scales: Dynamical approximations for composite quantum systems
• Quantum-Classical Dynamical Brackets
• From reasonable postulates to generalised Hamiltonian systems
• Observables and States p-Mechanics
• A Stepwise Planned Approach to the Solution of Hilbert's Sixth Problem. I : Noncommutative Symplectic Geometry and Hamiltonian Mechanics
• Exploring phonon-like interactions in one-dimensional Bose-Fermi mixtures
• Stochastic Thermodynamics at the Quantum-Classical Boundary: A Self-Consistent Framework Based on Adiabatic-Response Theory
• Universality of quantum symplectic structure
• Supmech: the Geometro-statistical Formalism Underlying Quantum Mechanics
• The dynamics of the Koopman-van Hove angular and linear momentum operators
• An illustration of canonical quantum-classical dynamics
• Hydrogen atom as a quantum-classical hybrid system