Complete positivity of nonlinear evolution: A case study
Quantum Physics
2009-10-30 v3 chao-dyn
funct-an
High Energy Physics - Theory
Functional Analysis
Chaotic Dynamics
Abstract
Simple Hartree-type equations lead to dynamics of a subsystem that is not completely positive in the sense accepted in mathematical literature. In the linear case this would imply that negative probabilities have to appear for some system that contains the subsystem in question. In the nonlinear case this does not happen because the mathematical definition is physically unfitting as shown on a concrete example.
Cite
@article{arxiv.quant-ph/9708029,
title = {Complete positivity of nonlinear evolution: A case study},
author = {Marek Czachor and Maciej Kuna},
journal= {arXiv preprint arXiv:quant-ph/9708029},
year = {2009}
}
Comments
extended version, 3 appendices added (on mixed states, projection postulate, nonlocality), to be published in Phys. Rev. A