Absorption in Invariant Domains for Semigroups of Quantum Channels

Carbone Raffaella; Girotti Federico

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Absorption in Invariant Domains for Semigroups of Quantum Channels

机译：Quantim群体的不变域中的吸收

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摘要

We introduce a notion of absorption operators in the context of quantum Markov processes. The absorption problem in invariant domains (enclosures) is treated for a quantum Markov evolution on a separable Hilbert space, both in discrete and continuous times: We define a well-behaving set of positive operators which can correspond to classical absorption probabilities, and we study their basic properties, in general, and with respect to accessibility structure of channels, transience and recurrence. In particular, we can prove that no accessibility is allowed between the null and positive recurrent subspaces. In the case, when the positive recurrent subspace is attractive, ergodic theory will allow us to get additional results, in particular about the description of fixed points.

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来源
《Annales Henri Poincare》 |2021年第8期|共34页
作者
Carbone Raffaella; Girotti Federico;
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作者单位

Univ Pavia Dipartimento Matemat Via Ferrata 1 I-27100 Pavia Italy;

Univ Pavia Dipartimento Matemat Via Ferrata 1 I-27100 Pavia Italy;

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原文格式 PDF
正文语种 eng
中图分类理论物理学;
关键词
Quantum channel; Quantum Markov semigroup; Absorption probabilities; Ergodic theory; Quantum recurrence; Fixed points;

机译：量子通道;量子马尔可夫半群;吸收概率;ergodic理论;量子复发;固定点;

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Absorption in Invariant Domains for Semigroups of Quantum Channels

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