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631.
632.
Frank Uhlig 《Numerical Linear Algebra with Applications》2023,30(6):e2513
This paper describes and develops a fast and accurate path following algorithm that computes the field of values boundary curve for every conceivable complex or real square matrix . It relies on the matrix flow decomposition algorithm that finds a proper block-diagonal flow representation for the associated hermitean matrix flow under unitary similarity if that is possible. Here is the 1-parameter-varying linear combination of the real and skew part matrices and of . For indecomposable matrix flows, has just one block and the ZNN based field of values algorithm works with directly. For decomposing flows , the algorithm decomposes the given matrix unitarily into block-diagonal form with diagonal blocks whose individual sizes add up to the size of . It then computes the field of values boundaries separately for each diagonal block using the path following ZNN eigenvalue method. The convex hull of all sub-fields of values boundary points finally determines the field of values boundary curve correctly for decomposing matrices . The algorithm removes standard restrictions for path following FoV methods that generally cannot deal with decomposing matrices due to possible eigencurve crossings of . Tests and numerical comparisons are included. Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and fast when compared with Johnson's Francis QR eigenvalue and Bendixson rectangle based method and compute global eigenanalyses of for large discrete sets of angles more slowly. 相似文献
633.
634.
Xue-Min Bai Xin-Yu Chen Jun-Jie Shi Xue-Yun Bai Jun-Qi Li Jiu-Qing Liang 《Annalen der Physik》2023,535(6):2300027
The quantum coherence of a two-qubit system in which each qubit is coupled to its own hierarchical environment is studied. The effect of the hierarchical environment is explored in order to improve the coherence effectively. It is discovered that the dynamics of coherence can be manipulated by the number N of the second-layer cavities (), the coupling strengths Ω0, Ω, κ, respectively for the qubit-cavity (m0), nearest-neighbor, and m0- cavities. It depends also on the decay rate Γ of second-layer cavities. Furthermore, an effective scheme for enhancing coherence is proposed by using weak measurement and weak measurement reversal. The explicit conditions of the optimal measurement strengths to improve the coherence comparatively are derived. It is seen that the final stable value of the coherence is independent of the number N of second-layer cavities but is related to the weak measurement strength m when the coupling strength between two nearest-neighbor cavities is taken into account. 相似文献