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Abstract
We formulate the dynamics of an infinitely extended open dissipative quantum system , Σ, in the Schroedinger picture. The generic model on which this is based comprises a C★-algebra, A , of observables, a folium, ℱ , of states on this algebra and a one-parameter semigroup, τ , of linear transformations of ℱ that represents its dynamics and is given by a natural infinite-volume limit of the corresponding semigroup for a finite system. On this basis, we establish that the dynamics of Σ is given by a one-parameter group of completely positive linear transformations of the W★-algebra dual to ℱ . This result serves to extend our earlier formulation [ 1 ] of infinitely extended conservative systems to open dissipative ones.
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