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Mini-Workshop: Product Systems and Independence in Quantum Dynamics

dc.date.accessioned2019-10-24T13:51:27Z
dc.date.available2019-10-24T13:51:27Z
dc.date.issued2009
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3111
dc.description.abstractQuantum dynamics, both reversible (i.e., closed quantum systems) and irreversible (i.e., open quantum systems), gives rise to product systems of Hilbert spaces or, more generally, of Hilbert modules. When we consider reversible dynamics that dilates an irreversible dynamics, then the product system of the latter is equal to the product system of the former (or is contained in a unique way). Whenever the dynamics is on a proper subalgebra of the algebra of all bounded operators on a Hilbert space, in particular, when the open system is classical (commutative) it is indispensable that we use Hilbert modules. The product system of a reversible dynamics is intimately related to a filtration of subalgebras that are independent in a state or conditionally independent in a conditional expectation of the reversible system. This has been illustrated in many concrete dilations that have been obtained with the help of quantum stochastic calculus. Here the underlying Fock space or module determines the sort of quantum independence underlying the reversible system. The mini-workshop brought together experts from quantum dynamics, product systems and quantum independence who have contributed to the general theory or who have studied intriguing examples. As the implications of the tight relationship between product systems and independence had so far been largely neglected, we expect from our mini-workshop a strong innovative impulse to this field.
dc.titleMini-Workshop: Product Systems and Independence in Quantum Dynamics
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWR-2009-9
local.series.idOWR-2009-9
local.subject.msc46
local.subject.msc60
local.subject.msc81
local.subject.msc16
local.sortindex551
local.date-range15 Feb - 21 Feb 2009
local.workshopcode0908b
local.workshoptitleMini-Workshop: Product Systems and Independence in Quantum Dynamics
local.organizersB.V. Rajarama Bhat, Bangalore; Uwe Franz, Besancon/Sendai; Michael Skeide, Campobasso
local.report-nameWorkshop Report 2009,9
local.opc-photo-id0908b
local.publishers-doi10.4171/OWR/2009/09
local.ems-referenceBhat B.V. Rajarama, Franz Uwe, Skeide Michael: Mini-Workshop: Product Systems and Independence in Quantum Dynamics. Oberwolfach Rep. 6 (2009), 493-548. doi: 10.4171/OWR/2009/09


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