Complete positivity of nonlinear evolution: A case study
arXiv:quant-ph/9708029 · doi:10.1103/PhysRevA.58.128
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.
extended version, 3 appendices added (on mixed states, projection postulate, nonlocality), to be published in Phys. Rev. A
References in corpus (6)
- Separability criterion and inseparable mixed states with positive partial transposition
- Nonlocal looking equations can make nonlinear quantum dynamics local
- Experimental limits on complete positivity from the K-K system
- Testing complete positivity
- Density matrix interpretation of solutions of Lie-Nambu equations
- Structure of nonlinear gauge transformations
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