A Problem of Powers and the Product of Spatial Product Systems
B. V. Rajarama Bhat, Volkmar Liebscher, Michael Skeide
TL;DR
This paper explores the Powers sum operation for spatial E0-semigroups, showing it corresponds to the product of spatial Arveson systems, which may differ from the tensor product, advancing understanding in quantum dynamics.
Contribution
It clarifies the relationship between Powers sum and the product of spatial Arveson systems, highlighting differences from the tensor product in quantum dynamics.
Findings
The Powers sum of spatial E0-semigroups equals the product of spatial Arveson systems.
The product may differ from the tensor product of Arveson systems.
The result is up to cocycle conjugacy, linking to spatial noises.
Abstract
In the 2002 AMS summer conference on ``Advances in Quantum Dynamics'' in Mount Holyoke Robert Powers proposed a sum operation for spatial E0-semigroups. Still during the conference Skeide showed that the Arveson system of that sum is the product of spatial Arveson systems. This product may but need not coincide with the tensor product of Arveson systems. The Powers sum of two spatial E0-semigroups is, therefore, up to cocycle conjugacy Skeide's product of spatial noises.
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