When two representations of the Lie algebra are coupled, the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states. These kernels have a connection with usual couplin...When two representations of the Lie algebra are coupled, the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states. These kernels have a connection with usual coupling coefficients. The explicit expressions of these kernels for SU(2), SO(4) and SUq(2) are given. When the direct product of three representations is formed in two ways, the recoupling integral kernels relating to the coupled group-related coherent states corresponding to two different schemes are introduced, and the relations between these kernels and the general recoupling coefficients are obtained. The properties of these kernels are discussed.展开更多
By means of improved ligand-field theory, the 'pure electronic' presure-induced shifts (PS's) and the PS's due to electron-phonon interaction (EPI) of the R1, R2, B1, B2, B3, and R'3 lines and the ...By means of improved ligand-field theory, the 'pure electronic' presure-induced shifts (PS's) and the PS's due to electron-phonon interaction (EPI) of the R1, R2, B1, B2, B3, and R'3 lines and the ground-state zero-field-splitting of ruby have been uniformly calculated. The calculation results are in very good agreement with all the experimental data. At normal pressure, ruby is a crystal with very strong crystal field. Thus, the admixture of |t22 (3T1)e4T2> and |t3 2 2 E> bases in the wavefunction of R1 level of ruby is small at normal pressure, and it gradually decreases with increasing pressure, which causes the R1-line PS of ruby to monotonously red shift with approximate linearity. The combined effect of the pure electronic PS of R1 line and the PS of R1 line due to EPI gives rise to the total PS of R1 line. The analyses and comparisons among the features of R1-line PS's of three laser crystals (ruby, GSGG:Cr3+ and GGG:Cr3+ ) have been made, and the origin of their difference has been revealed.展开更多
Representing the appeals of its industry,the high-tech interest group has recently become an emerging political force in the United States.With abundant financial resources and proficiency in political communication,t...Representing the appeals of its industry,the high-tech interest group has recently become an emerging political force in the United States.With abundant financial resources and proficiency in political communication,the group rapidly grows to be a significant force in the American political sphere.It has started to affect the internal and foreign affairs of the U.S.and played a proactive role in the latest presidential election.Since the high-tech interest group has already become and will continue to be a big player in Sino-U.S.relations,China should carefully deal with its appeals and conflict of interests,and try to develop this group into a stabilizer between the two countries.展开更多
Economic growth and environmental "friendliness" are the dual missions of China's grand western development. In the past eight years,China has seen the gap between eastern and western regions still widen...Economic growth and environmental "friendliness" are the dual missions of China's grand western development. In the past eight years,China has seen the gap between eastern and western regions still widening while also taking on the arduous task of protecting nature,ecology and environment in the western region. How has western development fared in the past eight years? What difficulties and challenges are being encountered? The development of the western region poses the single greatest difficulty facing China's regional economic development,but how can we advance along a "sound and fast" development path? The establishment of economic zones in Chengdu and Chongqing,Guanzhong and North Bay has opened up new possibilities and expectations for western China's economic development.展开更多
Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far...Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far away. In the recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the continuous symmetry breaks spontaneously. We expect that the violation of cluster property will be observed in other materials too, because the spontaneous symmetry breaking is found in many systems such as the high temperature superconductors and the superfluidity. In order to examine the cluster property for these materials, we studied a quantum nonlinear sigma model with U(1) symmetry in the previous work. There we showed that the model does have quasi-degenerate states. In this paper we study the quantum nonlinear sigma model with SU(2) symmetry. In our approach we first define the quantum system on the lattice and then adopt the representation where the kinetic term is diagonalized. Since we have no definition on the conjugate variable to the angle variable, we use the angular momentum operators instead for the kinetic term. In this representation we introduce the states with the fixed quantum numbers and carry out numerical calculations using quantum Monte Carlo methods and other methods. Through analytical and numerical studies, we conclude that the energy of the quasi-degenerate state is proportional to the squared total angular momentum as well as to the inverse of the lattice size.展开更多
文摘When two representations of the Lie algebra are coupled, the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states. These kernels have a connection with usual coupling coefficients. The explicit expressions of these kernels for SU(2), SO(4) and SUq(2) are given. When the direct product of three representations is formed in two ways, the recoupling integral kernels relating to the coupled group-related coherent states corresponding to two different schemes are introduced, and the relations between these kernels and the general recoupling coefficients are obtained. The properties of these kernels are discussed.
文摘By means of improved ligand-field theory, the 'pure electronic' presure-induced shifts (PS's) and the PS's due to electron-phonon interaction (EPI) of the R1, R2, B1, B2, B3, and R'3 lines and the ground-state zero-field-splitting of ruby have been uniformly calculated. The calculation results are in very good agreement with all the experimental data. At normal pressure, ruby is a crystal with very strong crystal field. Thus, the admixture of |t22 (3T1)e4T2> and |t3 2 2 E> bases in the wavefunction of R1 level of ruby is small at normal pressure, and it gradually decreases with increasing pressure, which causes the R1-line PS of ruby to monotonously red shift with approximate linearity. The combined effect of the pure electronic PS of R1 line and the PS of R1 line due to EPI gives rise to the total PS of R1 line. The analyses and comparisons among the features of R1-line PS's of three laser crystals (ruby, GSGG:Cr3+ and GGG:Cr3+ ) have been made, and the origin of their difference has been revealed.
文摘Representing the appeals of its industry,the high-tech interest group has recently become an emerging political force in the United States.With abundant financial resources and proficiency in political communication,the group rapidly grows to be a significant force in the American political sphere.It has started to affect the internal and foreign affairs of the U.S.and played a proactive role in the latest presidential election.Since the high-tech interest group has already become and will continue to be a big player in Sino-U.S.relations,China should carefully deal with its appeals and conflict of interests,and try to develop this group into a stabilizer between the two countries.
文摘Economic growth and environmental "friendliness" are the dual missions of China's grand western development. In the past eight years,China has seen the gap between eastern and western regions still widening while also taking on the arduous task of protecting nature,ecology and environment in the western region. How has western development fared in the past eight years? What difficulties and challenges are being encountered? The development of the western region poses the single greatest difficulty facing China's regional economic development,but how can we advance along a "sound and fast" development path? The establishment of economic zones in Chengdu and Chongqing,Guanzhong and North Bay has opened up new possibilities and expectations for western China's economic development.
文摘Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far away. In the recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the continuous symmetry breaks spontaneously. We expect that the violation of cluster property will be observed in other materials too, because the spontaneous symmetry breaking is found in many systems such as the high temperature superconductors and the superfluidity. In order to examine the cluster property for these materials, we studied a quantum nonlinear sigma model with U(1) symmetry in the previous work. There we showed that the model does have quasi-degenerate states. In this paper we study the quantum nonlinear sigma model with SU(2) symmetry. In our approach we first define the quantum system on the lattice and then adopt the representation where the kinetic term is diagonalized. Since we have no definition on the conjugate variable to the angle variable, we use the angular momentum operators instead for the kinetic term. In this representation we introduce the states with the fixed quantum numbers and carry out numerical calculations using quantum Monte Carlo methods and other methods. Through analytical and numerical studies, we conclude that the energy of the quasi-degenerate state is proportional to the squared total angular momentum as well as to the inverse of the lattice size.
