Quantum 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.
We wish to bring 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
have so far been largely neglected, we expect from this conference a
strong innovative impulse
to this field.
Ernst-Moritz-Arndt-Universität Greifswald |
Institut für Mathematik und Informatik |
Division for Algebra and Functional Analytic Applications |