Decoherence of hydrodynamic histories: A simple spin model
Abstract
In the context of the decoherent histories approach to the quantum mechanics of closed systems, GellMann 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 densitieshydrodynamic 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 onedimensional 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.
 Publication:

Physical Review D
 Pub Date:
 August 1996
 DOI:
 10.1103/PhysRevD.54.2899
 arXiv:
 arXiv:quantph/9601004
 Bibcode:
 1996PhRvD..54.2899B
 Keywords:

 03.65.Bz;
 75.10.Jm;
 98.80.Hw;
 Quantized spin models;
 Quantum Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 Standard TeX, 36 pages + 3 figures (postscript) Revised abstract and introduction. To appear in Physical Review D