1996/01/31 by Todd A. Brun, T. A. Brun, J. J. Halliwell · 37 citations
Computer Science · Mathematics · Physics and Astronomy · #Chain (unit) #Classical mechanics #Context (archaeology) #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum decoherence #Quantum mechanics #Simple (philosophy) #Spectroscopy and Quantum Chemical Studies #Spin (aerodynamics) #Spins #Statistical physics #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.54.2899
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 54(4), 2899-2912 (American Physical Society) · Standard TeX, 36 pages + 3 figures (postscript) Revised abstract and introduction. To appear in Physical Review D
arxiv created 1996/04/23 · openalex publication_date 1996/08/15 · arxiv updated 2014/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In the context of the decoherent histories approach to the quantum mechanics of closed systems, Gell-Mann and Hartle have argued that the variables typically characterizing the quasiclassical domain of a large complex system are the integrals over small volumes of locally conserved densities---hydrodynamic variables. The aim of this paper is to exhibit some simple models in which approximate decoherence arises as a result of local conservation. We derive a formula which shows the explicit connection between local conservation and approximate decoherence. We then consider a class of models consisting of a large number of weakly interacting components, in which the projections onto local densities may be decomposed into projections onto one of two alternatives of the individual components. The main example we consider is a one-dimensional chain of locally coupled spins, and the projections are onto the total spin in a subsection of the chain. We compute the decoherence functional for histories of local densities, in the limit when the number of components is very large. We find that decoherence requires two things: the smearing volumes must be sufficiently large to ensure approximate conservation, and the local densities must be partitioned into sufficiently large ranges to ensure protection against quantum fluctuations.