Weighted number operators on Bernoulli functionals and quantum exclusion semigroups
Weighted number operators on Bernoulli functionals and quantum exclusion semigroups
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伯努利泛函和量子排除半群上的加权数算子
DOI：
10.1063/1.5120102
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发表时间：
2019-11
影响因子：
1.3
通讯作者：
Suling Ren
中科院分区：
文献类型：
--
作者：
Caishi Wang;Yuling Tang;Suling Ren
量子伯努利噪声（QBN）是作用在伯努利泛函上的一类湮灭和产生算子，它们在等时间内满足正则反对易关系。本文首先利用QBN引入了一类作用在Bernoulli泛函上的自伴算子，我们称之为加权数算子。然后，我们明确了这些算子的谱分解，并建立了它们与湮灭算子和产生算子的对易关系。我们还得到了加权数算子有界的一个充要条件。最后，作为上述结果的应用，我们构造了一类与加权数算子相关的量子Markov半群，它们属于量子排斥半群范畴。量子Bernoulli噪声（QBN）是作用在Bernoulli泛函上的湮灭和产生算子族，它们在等时满足一个正则反对易关系。本文首先利用QBN引入了一类作用在Bernoulli泛函上的自伴算子，我们称之为加权数算子。然后，我们明确了这些算子的谱分解，并建立了它们与湮灭算子和产生算子的对易关系。我们还得到了加权数算子有界的一个充要条件。最后，作为上述结果的应用，我们构造了一类与加权数算子相关的量子Markov半群，它们属于量子排斥半群范畴。给出了这些量子马尔可夫半群的一些基本性质，并举例说明。
Quantum Bernoulli noises (QBN for short) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anticommutation relation in equal-time. In this paper, by using QBN, we first introduce a class of self-adjoint operators acting on Bernoulli functionals, which we call the weighted number operators. We then make clear spectral decompositions of these operators and establish their commutation relations with the annihilation as well as the creation operators. We also obtain a necessary and sufficient condition for a weighted number operator to be bounded. Finally, as an application of the above results, we construct a class of quantum Markov semigroups associated with the weighted number operators, which belong to the category of quantum exclusion semigroups. Some basic properties of these quantum Markov semigroups are shown and examples are given.Quantum Bernoulli noises (QBN for short) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anticommutation relation in equal-time. In this paper, by using QBN, we first introduce a class of self-adjoint operators acting on Bernoulli functionals, which we call the weighted number operators. We then make clear spectral decompositions of these operators and establish their commutation relations with the annihilation as well as the creation operators. We also obtain a necessary and sufficient condition for a weighted number operator to be bounded. Finally, as an application of the above results, we construct a class of quantum Markov semigroups associated with the weighted number operators, which belong to the category of quantum exclusion semigroups. Some basic properties of these quantum Markov semigroups are shown and examples are given.
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DOI：
10.1142/s0219025709003781
发表时间：
2009-09
期刊：
Infinite Dimensional Analysis, Quantum Probability and Related Topics
影响因子：
--
作者：
Leopoldo Pantaleón-Martínez;R. Quezada
通讯作者：
Leopoldo Pantaleón-Martínez;R. Quezada
DOI：
10.1007/978-3-662-21558-6
发表时间：
1993-03
期刊：
--
影响因子：
--
作者：
P. Meyer
通讯作者：
P. Meyer
DOI：
10.1007/978-3-662-03990-8
发表时间：
1999-10
期刊：
--
影响因子：
--
作者：
Thomas M. Liggett
通讯作者：
Thomas M. Liggett
影响因子：
1.7
作者：
A. Chebotarev;F. Fagnola
通讯作者：
A. Chebotarev;F. Fagnola
影响因子：
1.4
作者：
I. Nourdin;G. Peccati;G. Reinert
通讯作者：
I. Nourdin;G. Peccati;G. Reinert