Hybrid classical-quantum formulations ask for hybrid notions

Abstract

We reappraise some of the hybrid classical-quantum models proposed in the literature with the goal of retrieving some of their common characteristics. In particular, first, we analyze in detail the Peres-Terno argument regarding the inconsistency of hybrid quantizations of the Sudarshan type. We show that to accept such hybrid formalism entails the necessity of dealing with additional degrees of freedom beyond those in the straight complete quantization of the system. Second, we recover a similar enlargement of degrees of freedom in the so-called statistical hybrid models. Finally, we use Wigner's quantization of a simple model to illustrate how in hybrid systems the subsystems are never purely classical or quantum. A certain degree of quantumness (classicality) is being exchanged between the different sectors of the theory, which in this particular unphysical toy model makes them undistinguishable.

13 pages, 3 figures (minor changes to match the published version)

References in corpus (16)

• Decoherence, einselection, and the quantum origins of the classical
• Towards quantum superpositions of a mirror
• Linear dynamics of quantum-classical hybrids
• Hybrid classical-quantum dynamics
• Quantum Backreaction on ``Classical'' Variables
• Impediments to mixing classical and quantum dynamics
• Interacting classical and quantum ensembles
• Consistent classical and quantum mixed dynamics
• On the limits of quantum theory: contextuality and the quantum-classical cut
• Inconsistency of quantum--classical dynamics, and what it implies
• Absence of classical and quantum mixing
• Statistical consistency of quantum-classical hybrids
• Mixing quantum and classical mechanics and uniqueness of Planck's constant
• Statistics and Nosé formalism for Ehrenfest dynamics
• Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence
• Interacting classical and quantum particles

Cited by in corpus (36)

• Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity
• Koopman wavefunctions and classical-quantum correlation dynamics
• What gravity mediated entanglement can really tell us about quantum gravity
• Statistical moments for classical and quantum dynamics: formalism and generalized uncertainty relations
• Spin and localization of relativistic fermions and uncertainty relations
• Objective trajectories in hybrid classical-quantum dynamics
• Madelung transform and probability densities in hybrid classical-quantum dynamics
• The constraints of post-quantum classical gravity
• Classical and quantum behavior of the harmonic and the quartic oscillators
• Evolution of hybrid quantum-classical wavefunctions
• The classical-quantum limit
• Proliferation of observables and measurement in quantum-classical hybrids
• Canonical bracket in quantum-classical hybrid systems
• Newtonian Semiclassical Gravity in the Ghirardi-Rimini-Weber Theory with Matter Density Ontology
• When can localized spins interacting with conduction electrons in ferro- or antiferromagnets be described classically via the Landau-Lifshitz equation: Transition from quantum many-body entangled to quantum-classical nonequilibrium states
• Classicality of a quantum oscillator
• Is it time to rethink quantum gravity?
• Projective representation of the Galilei group for classical and quantum-classical systems
• Derivation of quantum theory with superselection rules
• Vindication of entanglement-based witnesses of non-classicality in hybrid systems
• Restricting loop expansions in gauge theories coupled to matter
• Quantum F_un: the q=1 Limit of Galois Field Quantum Mechanics, Projective Geometry, and the Field with One Element
• Quantum-Classical Dynamical Brackets
• Phase space quantum-classical hybrid model
• Semiclassical gravity beyond coherent states
• The Schwinger action principle for classical systems
• A New Approach to Generalised Uncertainty Relations
• Galilean covariance of quantum-classical hybrid systems of the Sudarshan type
• Ehrenfest principle and unitary dynamics of quantum-classical systems with general potential interaction
• Phase space hybrid theory of quantum measurement with nonlinear and stochastic dynamics
• Unitary representation of the Poincaré group for classical relativistic dynamics
• Hybrid quantum-classical systems: statistics, entropy, microcanonical ensemble and its connection to the canonical ensemble
• Stochastic Thermodynamics at the Quantum-Classical Boundary: A Self-Consistent Framework Based on Adiabatic-Response Theory
• Restoring the second law to classical-quantum dynamics
• Mixed quantal-semiquantal dynamics with stochastic particles for backreaction
• An illustration of canonical quantum-classical dynamics