Utilizing the results that the Faddeev model is equivalent to the mesonic sector of the SU（2） Skyrme model, where the baryon number current vanishes everywhere, some exact solutions including the vortex solutions of...Utilizing the results that the Faddeev model is equivalent to the mesonic sector of the SU（2） Skyrme model, where the baryon number current vanishes everywhere, some exact solutions including the vortex solutions of the Faddeev model axe discussed. The solutions are classified by the 2, the new multisoliton solutions are obtained and the pipe shape found. first Chern number. When the Chern number equals distribution of the energy density of the solutions are展开更多
We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space R^1＋n to the unit sphere S2, which obey a system of non-linear wave equations. The nonlinearity enjoys the ...We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space R^1＋n to the unit sphere S2, which obey a system of non-linear wave equations. The nonlinearity enjoys the null structure and contains semi-linear terms, quasi-linear terms and unknowns themselves. We prove that the Cauchy problem is globally well-posed for sufficiently small initial data in Sobolev space.展开更多
The Faddeev model is a fundamental model in relativistic quantum field theory used to model elementary particles. The Faddeev model can be regarded as a system of non-linear wave equations with both quasi-linear and s...The Faddeev model is a fundamental model in relativistic quantum field theory used to model elementary particles. The Faddeev model can be regarded as a system of non-linear wave equations with both quasi-linear and semi-linear non-linearities, which is particularly challenging in two space dimensions. A key feature of the system is that there exist undifferentiated wave components in the non-linearities, which somehow causes extra difficulties. Nevertheless, the Cauchy problem in two space dimenions was tackled by Lei-Lin-Zhou(2011) with small, regular, and compactly supported initial data, using Klainerman’s vector field method enhanced by a novel angular-radial anisotropic technique.In the present paper, the authors revisit the Faddeev model and remove the compactness assumptions on the initial data by Lei-Lin-Zhou(2011). The proof relies on an improved L2norm estimate of the wave components in Theorem 3.1 and a decomposition technique for non-linearities of divergence form.展开更多
Using the Faddeev-Jackiw （FJ） quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which ...Using the Faddeev-Jackiw （FJ） quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which agree with the results obtained by using the Dirac＇s method.展开更多
The neutron-halo nuclei, ^11Li, ^14Be, and ^17B, are studied in the three-body model. The Yukawainteraction is used to describe the interaction of the two-body subsystem. For given parameters ot the twobody interactio...The neutron-halo nuclei, ^11Li, ^14Be, and ^17B, are studied in the three-body model. The Yukawainteraction is used to describe the interaction of the two-body subsystem. For given parameters ot the twobody interaction, the properties of these neutron-halo nuclei are calculated with the Faddeev equations and the results are compared with those in the variational method. It is shown that the method of the Faddeev equations is more accurate. Then the dependencies of the two- and three-body energies on the parameters are studied. We find numerically that two- and three-body correlations differ greatly from each other with the variation of the intrinsic force range.展开更多
基金National Natural Science Foundation of China under Grant No.10601031the Natural Science Foundation of Shanghai Municipal Education Commission under Grant No.05LZ08the Foundation of Shanghai University of Electric Power under Grant No.K2005-01
文摘Utilizing the results that the Faddeev model is equivalent to the mesonic sector of the SU（2） Skyrme model, where the baryon number current vanishes everywhere, some exact solutions including the vortex solutions of the Faddeev model axe discussed. The solutions are classified by the 2, the new multisoliton solutions are obtained and the pipe shape found. first Chern number. When the Chern number equals distribution of the energy density of the solutions are
基金The first author is partly supported by National Natural Science Foundation of China （Grants Nos. 10801029 and 10911120384）, FANEDD, Shanghai Rising Star Program （10QA1400300）, SGST 09DZ2272900 and SRF for ROCS, SEM the second author is partly supported by an NSF grant the third author is partly supported by the National Natural Science Foundation of China （Crant No. 10728101）, the 973 project of the Ministry of Science and Technology of China, the Doctoral Program Foundation of the Ministry of Education of China, the ＂111＂ project （B08018） and SGST 09DZ2272900Acknowledgements Part of the work was carried out when Zhen Lei was visiting the Courant Institute. He would like to thank Professor Fanghua Lin for his hospitality.
文摘We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space R^1＋n to the unit sphere S2, which obey a system of non-linear wave equations. The nonlinearity enjoys the null structure and contains semi-linear terms, quasi-linear terms and unknowns themselves. We prove that the Cauchy problem is globally well-posed for sufficiently small initial data in Sobolev space.
基金supported by the National Natural Science Foundation of China(No.11725102)the China Postdoctoral Science Foundation(No.2021M690702)+1 种基金the National Support Program for Young Top-Notch TalentsShanghai Science and Technology Program(Nos.21JC1400600,19JC1420101)。
文摘The Faddeev model is a fundamental model in relativistic quantum field theory used to model elementary particles. The Faddeev model can be regarded as a system of non-linear wave equations with both quasi-linear and semi-linear non-linearities, which is particularly challenging in two space dimensions. A key feature of the system is that there exist undifferentiated wave components in the non-linearities, which somehow causes extra difficulties. Nevertheless, the Cauchy problem in two space dimenions was tackled by Lei-Lin-Zhou(2011) with small, regular, and compactly supported initial data, using Klainerman’s vector field method enhanced by a novel angular-radial anisotropic technique.In the present paper, the authors revisit the Faddeev model and remove the compactness assumptions on the initial data by Lei-Lin-Zhou(2011). The proof relies on an improved L2norm estimate of the wave components in Theorem 3.1 and a decomposition technique for non-linearities of divergence form.
文摘Using the Faddeev-Jackiw （FJ） quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which agree with the results obtained by using the Dirac＇s method.
基金Supported by National Natural Science Foundation of China (10535010, 10775068) 973 National Major State Basic Research and Development of China (2007CB815004)+2 种基金CAS Knowledge Innovation Project (KJCX2-SW-N02) Research Fund of Education Ministry under contract RFDP (20070284016)Green-Blue Project of Jiangsu Province
文摘The neutron-halo nuclei, ^11Li, ^14Be, and ^17B, are studied in the three-body model. The Yukawainteraction is used to describe the interaction of the two-body subsystem. For given parameters ot the twobody interaction, the properties of these neutron-halo nuclei are calculated with the Faddeev equations and the results are compared with those in the variational method. It is shown that the method of the Faddeev equations is more accurate. Then the dependencies of the two- and three-body energies on the parameters are studied. We find numerically that two- and three-body correlations differ greatly from each other with the variation of the intrinsic force range.
