Large Deviations for Quantum Markov Semigroups on the 2 × 2-Matrix Algebra
Large Deviations for Quantum Markov Semigroups on the 2 × 2-Matrix Algebra
复制标题
2×2矩阵代数上量子马尔可夫半群的大偏差
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
H. Comman
中科院分区：
文献类型：
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作者：
H. Comman
设$$（{mathcal{T}}_{*t}）$$是作用在全2 × 2-矩阵代数上的具有吸收纯态的预对偶量子Markov半群。证明了对于任意初始状态ω，表示状态网（{mathcal{T}}_{*t}（omega））的正交测度网满足纯状态空间中的大偏差原理，其速率函数以生成元的形式给出，且不依赖于ω.这意味着$$（{mathcal{T}}_{*t}（omega））$$对所有足够大的t都是忠实的。研究了在弱耦合极限下出现的例子。
Abstract.Let $$({mathcal{T}}_{*t})$$ be a predual quantum Markov semigroup acting on the full 2 × 2-matrix algebra and having an absorbing pure state. We prove that for any initial state ω, the net of orthogonal measures representing the net of states $$({mathcal{T}}_{*t}(omega))$$ satisfies a large deviation principle in the pure state space, with a rate function given in terms of the generator, and which does not depend on ω. This implies that $$({mathcal{T}}_{*t}(omega))$$ is faithful for all t large enough. Examples arising in weak coupling limit are studied.