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A Remark on the structure of symmetric quantum dynamical semigroups on von Neumann algebras | | Sergio Albeverio
; Debashish Goswami
; | | Date: |
30 Jul 2002 | | Subject: | Mathematical Physics; Functional Analysis | math-ph math.FA math.MP | | 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. | | Source: | arXiv, math-ph/0207047 | | Services: | Forum | Review | PDF | Favorites | |
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