This paper concerns the number and distributions of limit cycles in a Z 2-equivariant quintic planar vector field. 25 limit cycles are found in this special planar polynomial system and four different configurations o...This paper concerns the number and distributions of limit cycles in a Z 2-equivariant quintic planar vector field. 25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation. It can be concluded that H(5) ? 25 = 52, where H(5) is the Hilbert number for quintic polynomial systems. The results obtained are useful to study the weakened 16th Hilbert problem.展开更多
We theoretically investigate the features of two-photon absorption in a coherently driven four-level atomic system with closed-loop configuration. It is found that two-photon absorption can be completely suppressed ju...We theoretically investigate the features of two-photon absorption in a coherently driven four-level atomic system with closed-loop configuration. It is found that two-photon absorption can be completely suppressed just by properly adjusting the relative phase of four coherent low-intensity driving fields and the atomic system becomes trans- parent against two-photon absorption. From a physical point of view, we explicitly explain these results in terms of quantum interference induced by two different two-photon excitation channels.展开更多
基金Supported by the Fund of Youth of Jiangsu University(Grant No.05JDG011)the National Natural Science Foundation of China(Nos.90610031,10671127)+1 种基金the Outstanding Personnel Program in Six Fields of Jiangsu Province(Grant No.6-A-029)Shanghai Shuguang Genzong Project(Grant No.04SGG05)
文摘This paper concerns the number and distributions of limit cycles in a Z 2-equivariant quintic planar vector field. 25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation. It can be concluded that H(5) ? 25 = 52, where H(5) is the Hilbert number for quintic polynomial systems. The results obtained are useful to study the weakened 16th Hilbert problem.
基金The project supported in part by National Natural Science Foundation of China unde.r Grant Nos. 10634060, 10575040, and 90503010 Acknowledgments The authors would like to thank professor Ying WU for helpful discussion and his encouragement.
文摘We theoretically investigate the features of two-photon absorption in a coherently driven four-level atomic system with closed-loop configuration. It is found that two-photon absorption can be completely suppressed just by properly adjusting the relative phase of four coherent low-intensity driving fields and the atomic system becomes trans- parent against two-photon absorption. From a physical point of view, we explicitly explain these results in terms of quantum interference induced by two different two-photon excitation channels.
