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81.
Motivated by their frequent use in quantum mechanical studies of entanglement, we give a brief overview of Schmidt modes and Schmidt decompositions of two-particle wave functions. We discuss methods of their derivation and include a little-known approach used in the original work by E. Schmidt [Math. Annalen, 63 (1906), 433]. This employs the bipartite wave function itself rather than the more complicated two-party reduced density matrix. As an illustration, Schmidt modes for two-photon polarisation qutrits are derived in a general form. The derivation is accompanied by a series of simple examples with special choices of parameters. Relationships between Schmidt modes, polarisation Stokes vectors and entanglement are also discussed. 相似文献
82.
An approach to highly enhance the compression efficiency of the integral images by applying the Karhunen-Loeve transform (KLT) algorithm to the motion-compensated sub-images is proposed. The sub-images transformed from the elemental images picked-up from the three-dimensional (3D) object might represent the different perspectives of the object. Thus, the similarity among the sub-images gets better than that among the elemental images, so that an improvement of compression efficiency of the sub-images could be obtained. However, motion vectors occurred among the sub-images might result in an additional increase of image data to be compressed. Accordingly, in this paper, motion vectors have been estimated and compensated in all sub-image in advance. Then the KLT algorithm was applied to these motion-compensated sub-images for compression. It is shown from some experimental results that compression efficiency of the proposed method has been improved up to 24.44%, 40.62%, respectively, on the average compared to that of the conventional KLT compression method and that of the JPEG. 相似文献
83.
Relativistic resonances and decaying states are described by representations of Poincaré transformations, similar to Wigner's definition of stable particles. To associate decaying state vectors to resonance poles of the S‐matrix, the conventional Hilbert space assumption (or asymptotic completeness) is replaced by a new hypothesis that associates different dense Hardy subspaces to the in‐ and out‐scattering states. Then one can separate the scattering amplitude into a background amplitude and one or several “relativistic Breit‐Wigner” amplitudes, which represent the resonances per se. These Breit‐Wigner amplitudes have a precisely defined lineshape and are associated to exponentially decaying Gamow vectors which furnish the irreducible representation spaces of causal Poincaré transformations into the forward light cone. 相似文献
84.
Keisuke Araki 《Optical Review》2000,7(3):221-229
We have established a new method of aberration analysis for off-axial optical systems which are generalized concepts of co-axial optical systems, by introducing two kinds of newly defined 4-element vectors and expanding these vectors with the help of tensor algebra. In this method, since aberration properties are represented in tensor form, we can easily formulate the aberration relations between different azimuths. We can then evaluate the azimuth dependence of aberration properties in greater detail by separating them into inherent optical properties parts, which are independent of azimuths, and the paraxial ray-tracing part, which includes the expression of the evaluation azimuth. 相似文献
85.
Based on the Husimi operator in pure state form introduced by Fan et al., which is a squeezed coherent state projector, and the technique ofintegration within an ordered product (IWOP) of operators, as well as theentangled state representations, we obtain the Husimi functions of theexcited squeezed vacuum states (ESVS) and two marginal distributions of theHusimi functions of the ESVS. 相似文献
86.
87.
Il Bong Jung Alan Lambert Jan Stochel 《Proceedings of the American Mathematical Society》2004,132(8):2291-2302
The concept of backward extension for subnormal weighted shifts is generalized to arbitrary subnormal operators. Several differences and similarities in these contexts are explored, with emphasis on the structure of the underlying measures.
88.
89.
在很多实际应用中需要计算大规模矩阵的若干个最小奇异组.调和投影方法是计算内部特征对的常用方法,其原理可用于求解大规模奇异值分解问题.本文证明了,当投影空间足够好时,该方法得到的近似奇异值收敛,但近似奇异向量可能收敛很慢甚至不收敛.根据第二作者近年来提出的精化投影方法的原理,本文提出一种精化的调和Lanczos双对角化方法,证明了它的收敛性.然后将该方法与Sorensen提出的隐式重新启动技术相结合,开发出隐式重新启动的调和Lanczos双对角化算法(IRHLB)和隐式重新启动的精化调和Lanczos双对角化算法(IRRHLB).位移的合理选取是算法成功的关键之一,本文对精化算法提出了一种新的位移策略,称之为\"精化调和位移\".理论分析表明,精化调和位移比IRHLB中所用的调和位移要好,且可以廉价可靠地计算出来.数值实验表明,IRRHLB比IRHLB要显著优越,而且比目前常用的隐式重新启动的Lanczos双对角化方法(IRLB)和精化算法IRRLB更有效. 相似文献
90.
在感应型速调管调制器中使用了纳米晶磁性材料制作大尺寸磁环,使用伏安向量法对材料试样的磁性能进行测量,得到频率为20.03 kHz和50 kHz时的动态磁化曲线、磁导率、磁场损耗等参数。使用脉冲法对成型的大尺寸磁环动态磁性能进行测量,励磁方式和工作中完全一致,在测量脉冲脉宽3.5~4.0 μs,重复频率50 Hz,初次线圈均为1匝,外径220 mm,内径80 mm,高60 mm,截面积4 200 mm2时,得到磁环实际能够达到的伏秒数为0.007 V·s,此时所需的偏磁电流大小为8 A。 相似文献