论文标题
量子动态的半群和更大的希尔伯特空间的教堂
Quantum-Dynamical Semigroups and the Church of the Larger Hilbert Space
论文作者
论文摘要
在这项工作中，我们调查了量子动物半群的刺激性扩张，已知通过70年代初期戴维斯（Davies）给出的建设性证明而存在。我们表明，如果Semigroup描述了一个开放系统，也就是说，如果它不仅由单一渠道组成，那么扩张的封闭系统的演变就必须由无限的Hamiltonian产生。随后，无论原始系统如何，环境都必须对应于无限的希尔伯特空间。此外，我们证明，具有界限的Hamiltonian的STINESPRING扩张的第二个导数产生了某些量子动力学半群的耗散部分，反之亦然。特别是这表征了量子动力学半群的发电机，这是通过刺激性扩张的。
In this work we investigate Stinespring dilations of quantum-dynamical semigroups, which are known to exist by means of a constructive proof given by Davies in the early 70s. We show that if the semigroup describes an open system, that is, if it does not consist of only unitary channels, then the evolution of the dilated closed system has to be generated by an unbounded Hamiltonian; subsequently the environment has to correspond to an infinite-dimensional Hilbert space, regardless of the original system. Moreover, we prove that the second derivative of Stinespring dilations with a bounded total Hamiltonian yields the dissipative part of some quantum-dynamical semigroup -- and vice versa. In particular this characterizes the generators of quantum-dynamical semigroups via Stinespring dilations.
