Impediments to mixing classical and quantum dynamics

1998/12/31 by J. Caro, L. L. Salcedo · 1 voice · 5 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #quant-ph

paper · pdf · doi:10.1103/physreva.60.842

published as Phys.Rev. A60 (1999) 842-852 · RevTex, 21 pages. Title slightly modified and summary section added

arxiv created 1999/04/30 · openalex publication_date 1999/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

Citations

• Absence of classical and quantum mixing

Cited by

• Inconsistency of quantum--classical dynamics, and what it implies
• The dynamics of the Koopman-van Hove angular and linear momentum\n operators
• A quantum-classical bracket from p -mechanics
• Is quantum gravity necessary?
• Linear dynamics of quantum-classical hybrids

Discussions

• The situation you're referring to is classical / quantum hybridization. There are no-go theorems pertaining to this: “Inconsistency of linear dynamics and Born’s rule” (2021), Phys. Rev. A 104, 052224 [stackexchange, 0 points]