A Remark on the structure of symmetric quantum dynamical semigroups on von Neumann algebras
Abstract
We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant (i.e. type I von Neumann algebras), we give a necessary and sufficient algebraic condition for the generator of such a semigroup to be written as a sum of square of self-adjoint derivations of the von Neumann algebra. This generalizes some of the results obtained by Albeverio, H(phi)egh-Krohn and Olsen [Alb] for the special case of the finite dimensional matrix algebras. We also study similar questions for a class of quantum dynamical semigroups with unbounded generators.
Keywords
Cite
@article{arxiv.math-ph/0207047,
title = {A Remark on the structure of symmetric quantum dynamical semigroups on von Neumann algebras},
author = {Sergio Albeverio and Debashish Goswami},
journal= {arXiv preprint arXiv:math-ph/0207047},
year = {2007}
}
Comments
accepted in Infinite Dimensional Analysis, Quantum Probability and Related Toplics (World Scientific)