| 三自旋1/2量子控制系统的伴随矩阵计算 |
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| 引用本文： | 周绍生,李家虎,王从江. 三自旋1/2量子控制系统的伴随矩阵计算[J]. 杭州电子科技大学学报, 2014, 0(3): 1-8 |
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| 作者姓名： | 周绍生 李家虎 王从江 |
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| 作者单位： | [1]杭州电子科技大学信息与控制研究所,浙江杭州310018 [2]杭州电子科技大学理学院,浙江杭州310018 |
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| 基金项目： | 国家自然科学基金资助项目（61273093）; 浙江省自然科学基金资助项目（LZ12F03001） |
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| 摘 要： | 将关于密度算子的Liouville-von Neumann方程表示成坐标微分方程,伴随矩阵具有重要作用。对于三自旋1/2量子系统需要64个64×64的伴随矩阵来描述其坐标动态。基于已建立的多自旋1/2量子系统的伴随矩阵和反伴随矩阵的计算公式,该文给出了三自旋1/2量子系统的几个伴随矩阵和反伴随矩阵的算例。计算结果表明,这些64维的伴随矩阵和反伴随矩阵均是稀疏矩阵。通过计算将这些矩阵的非零元列举在表格中并讨论了非零元的分布。
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| 关 键 词： | 自旋量子系统 伴随与反伴随矩阵 李代数 张量积 泡利矩阵 |
Computation of Adjoint Matrices in Three-spin 1/2 Quantum Control Systems |
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| Shaosheng Zhou,Jiahu Li,Congjiang Wang. Computation of Adjoint Matrices in Three-spin 1/2 Quantum Control Systems[J]. Journal of Hangzhou Dianzi University, 2014, 0(3): 1-8 |
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| Authors: | Shaosheng Zhou Jiahu Li Congjiang Wang |
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| Affiliation: | 1. Institute of Information and Control, Hangzhou Dianzi University, Hangzhou Zhejiang 310018, China; 2. Science School, Hangzhou Dianzi University, Hangzhou Zhejiang 310018, China) |
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| Abstract: | The adjoint matrices play an important role in the coordinate differential equation transformed from the Liouville-von Neumann equation for a density operator. In order to characterize the dynamics of the coordinates of the density operator in three-spin 1 /2 systems,64 adjoint matrices,which are 64 dimensional, need to be computed. Based on the established computational formulas of adjoint and anti-adjoint matrices in multi-spin 1 /2 systems,the computational examples of some adjoint and anti-adjoint matrices are given in three-spin 1 /2 systems. The results of the examples reveal these matrices are sparse. All the nonzero entries of these sparse matrices are listed in tables and the distribution of the nonzero entries in each 64 × 64 matrix is discussed as well. |
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| Keywords: | spin system adjoint and anti-adjoint matrix Lie algebra tensor product Pauli matrix |
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