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, $\mathcal{A}$, 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.

我们在Schroedinger图片中制定了无限扩展的开放耗散量子系统Σ的动力学。该模型所基于的通用模型包括C ^★-代数， $\mathcal{一种}$，可观察到的，大叶 $ℱ$表示该代数上的状态，以及一参数半群τ的线性变换 $ℱ$表示其动力学，并由有限系统相应半群的自然无穷极限给出。在此基础上，我们确定Σ的动力学由W ^★-代数对偶 的完全正线性变换的一参数组给出$ℱ$。该结果有助于将我们先前对无限扩展的保守系统的公式[1]扩展为开放的耗散系统。