Bernoulli泛函上典则酉对合的扰动

数学物理学报 ›› 2022, Vol. 42 ›› Issue (4): 969-977.

Bernoulli泛函上典则酉对合的扰动

范楠,王才士*(),姬红

西北师范大学数学与统计学院兰州 730070

收稿日期:2021-07-29 出版日期:2022-08-26 发布日期:2022-08-08
通讯作者: 王才士 E-mail:wangcs@nwnu.edu.cn
基金资助:
国家自然科学基金(11861057)

Perturbations of Canonical Unitary Involutions Associated with Quantum Bernoulli Noises

Nan Fan,Caishi Wang*(),Hong Ji

School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070

Received:2021-07-29 Online:2022-08-26 Published:2022-08-08
Contact: Caishi Wang E-mail:wangcs@nwnu.edu.cn
Supported by:
the NSFC(11861057)

摘要/Abstract

摘要：

量子Bernoulli噪声(QBN) 是平方可积Bernoulli泛函空间上的湮灭和增生算子, 满足一种等时的典则反交换关系(CAR), 在开放量子系统的研究中有着重要应用.该文研究一类与QBN有关的典则酉对合的扰动, 从算子谱理论的观点分析了这类扰动作为算子的谱, 精确得到了它们的谱和点谱, 并给出了相应的特征子空间的构造.作为应用, 该文也讨论了以此类扰动作为演化算子的抽象量子游荡, 得到了该抽象量子游荡的无穷多个平稳分布.

关键词: 量子概率, 量子Bernoulli噪声, 酉对合的扰动, 谱, 量子游荡

Abstract:

Quantum Bernoulli noises (QBN) are annihilation and creation operators acting on the space of square integrable Bernoulli functionals, which satisfy a canonical anti-commutation relation (CAR) in equal time and can play an important role in describing the environment of an open quantum system. In this paper, we address a type of perturbations of the canonical unitary involutions associated with QBN. We analyze these perturbations from a perspective of spectral theory and obtain exactly their spectra, which coincide with their point spectra. We also discuss eigenvectors of these perturbations from an algebraic point of view and unveil the structures of the subspaces consisting of their eigenvectors. Finally, as application, we consider the abstract quantum walks driven by these perturbations and obtain infinitely many invariant probability distributions of these walks.

Key words: Quantum probability, Quantum Bernoulli noise, Perturbation of unitary involution, Spectrum, Quantum walk

中图分类号:

O211.6

范楠,王才士,姬红. Bernoulli泛函上典则酉对合的扰动[J]. 数学物理学报, 2022, 42(4): 969-977.

Nan Fan,Caishi Wang,Hong Ji. Perturbations of Canonical Unitary Involutions Associated with Quantum Bernoulli Noises[J]. Acta mathematica scientia,Series A, 2022, 42(4): 969-977.

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