1995/04/24 by Reinhard F. Werner, R. F. Werner, Werner, R. F. · 3 citations
Computer Science · Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum many-body systems #cond-mat #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9504016
plain TeX, 33 pages, no figures
arxiv created 1995/04/24 · openalex publication_date 1995/04/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a quantum observable A_ℏ depending on a parameter ℏ we define the notion ``A_ℏ converges in the classical limit''. The limit is a function on phase space. Convergence is in norm in the sense that A_ℏ→0 is equivalent with \Vert A_ℏ\Vert→0. The ℏ-wise product of convergent observables converges to the product of the limiting phase space functions. ℏ-1 times the commutator of suitable observables converges to the Poisson bracket of the limits. For a large class of convergent Hamiltonians the ℏ-wise action of the corresponding dynamics converges to the classical Hamiltonian dynamics. The connections with earlier approaches, based on the WKB method, or on Wigner distribution functions, or on the limits of coherent states are reviewed.