Bernoulli泛函空间中截断计数算子的时间算子
The Time Operator of the TruncationOperator of the Number Operator Actingon Bernoulli Functional
DOI: 10.12677/PM.2023.131002, PDF, HTML, 下载: 154  浏览: 296  国家自然科学基金支持
作者: 杨 婷, 张丽霞, 王才士#:西北师范大学数学与统计学院,甘肃 兰州
关键词: 计数算子时间算子量子Bernoulli 噪声Number Operator Time Operator Quantum Bernoulli Noise C
摘要: 本文利用自伴算子的时间算子理论,初步构造了Bernoulli 泛函空间中与量子Bernoulli 噪声有密切联系的计数算子其截断算子的时间算子,且证明该时间算子并不唯一。
Abstract: In this paper, using the time operator theory of self-adjoint operator, we construct the time of the truncation operator of the number operator acting on Bernoulli functional which is closely related to the quantum Bernoulli noise and prove that the the time operator is not unique.
文章引用:杨婷, 张丽霞, 王才士. Bernoulli泛函空间中截断计数算子的时间算子[J]. 理论数学, 2023, 13(1): 15-23. https://doi.org/10.12677/PM.2023.131002

参考文献

[1] Privault, N. (2008) Stochastic Analysis of Bernoulli Processes. Probability Surveys, 5, 435-483.
https://doi.org/10.1214/08-PS139
[2] Wang, C.S., Lu, Y.C. and Chai, H.F. (2011) An Alternative Approach to Privault's Discrete- Time Chaotic Calculus. Journal of Mathematical Analysis and Applications, 373, 643-654.
https://doi.org/10.1016/j.jmaa.2010.08.021
[3] Wang, C.S. and Chen, J.S. (2016) Quantum Markov Semigroups Constructed from Quantum Bernoulli Noises. Journal of Mathematical Physics, 57, Article ID: 023502.
https://doi.org/10.1063/1.4939920
[4] Arai, A. and Matsuzawa, Y. (2008) Time Operators of a Hamiltonian with Purely Discrete Spectrum. Reviews in Mathematical Physics, 20, 951-978.
https://doi.org/10.1142/S0129055X08003481
[5] Pauli, W. (2012) General Principles of Quantum Mechanics. Springer Science Business Media, Berlin.
[6] Aharonov, Y. and Bohm, D. (1961) Time in the Quantum Theory and the Uncertainty Relation for Time and Energy. Physical Review, 122, 1649-1658.
https://doi.org/10.1103/PhysRev.122.1649
[7] Arai, A. (2009) Necessary and Sufficient Conditions for a Hamiltonian with Discrete Eigenvalues to Have Time Operators. Letters in Mathematical Physics, 87, 67-80.
https://doi.org/10.1007/s11005-008-0286-z
[8] Wang, C.S., Chai, H.F. and Lu, Y.C. (2010) Discrete-Time Quantum Bernoulli Noises. Journal of Mathematical Physics, 51, Article ID: 053528.
https://doi.org/10.1063/1.3431028
[9] Wang, C.S. and Ye, X.J. (2016) Quantum Walk in Terms of Quantum Brnoulli Noises. Quantum Information Process, 15, 1897-1908.
https://doi.org/10.1007/s11128-016-1259-2
[10] Arai, A. (2020) Inequivalent Representations of Canonical Commutation and Anti- Commutation Relations: Representation-theoretical Viewpoint for Quantum Phenomena. Springer Nature, Berlin.