In <span style="font-family:;" "="">the </span><span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of...In <span style="font-family:;" "="">the </span><span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of the lithium atom and l</span><span style="font-family:;" "="">ithium like ions up to <i>Z</i> = 10 in an external strong magnetic field are evaluated. Furthermore, the two low-lying excited states <img src="Edit_d92f9e9d-e574-4fa3-91fb-a153db020509.png" alt="" /></span><span style="font-family:;" "="">, <span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><img src="data:image/png;base64,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" alt="" /> <img src="Edit_5bf0039b-89f7-4346-a3cb-178f5df359cf.png" width="0" height="0" alt="" /><img src="data:image/png;base64,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" alt="" /><img src="Edit_41f9b122-3fdc-4f01-9470-542944413516.png" alt="" /></span><span style="font-family:;" "="">and <img src="data:image/png;base64,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" alt="" /><span></span></span><span style="font-family:;" "=""><span> <img src="Edit_79f5e8c8-0b24-4dfd-8b9e-080183cc967f.png" alt="" /></span>of the lithium atom in strong magnetic field are also investigated</span><span style="font-family:;" "="">. </span><span style="font-family:;" "="">Simple trial wave functions for lithium are used.</span>展开更多
In this study, we show how to generalize Hirshfeld partitioning methods to possibly include non-spherical proatom densities. While this generalization is numerically challenging(requiring global optimization of a larg...In this study, we show how to generalize Hirshfeld partitioning methods to possibly include non-spherical proatom densities. While this generalization is numerically challenging(requiring global optimization of a large number of parameters), it is conceptually appealing because it allows the proatoms to be pre-polarized, or even promoted, to a state that more closely resembles the atom in a molecule. This method is based on first characterizing the convex set of proatom densities associated with the degenerate ground states of isolated atoms and atomic ions. The preferred orientation of the proatoms' densities are then obtained by minimizing the information–theoretic distance between the promolecular and molecular densities. If contributions from excited states(and not just degenerate ground states) are included in the convex set, this method can describe promoted atoms. While the procedure is intractable in general, if one includes only atomic states that have differing electron-numbers and/or spins, the variational principle becomes a simple convex optimization with a single unique solution.展开更多
The ground states of the ultracold spin-1 atoms trapped in a deep one-dimensional double-well optical superlattice in a weak magnetic field are obtained. It is shown that the ground-state diagrams of the reduced doubl...The ground states of the ultracold spin-1 atoms trapped in a deep one-dimensional double-well optical superlattice in a weak magnetic field are obtained. It is shown that the ground-state diagrams of the reduced double- well model are remarkably different for the antiferromagnetic and ferromagnetic condensates. The transition between the singlet state and nematic state is observed for the antiferromagnetic interaction atoms, which can be realized by modulating the tunneling parameter or the quadratic Zeeman energy. An experiment to distinguish the different spin states is suggested.展开更多
文摘In <span style="font-family:;" "="">the </span><span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of the lithium atom and l</span><span style="font-family:;" "="">ithium like ions up to <i>Z</i> = 10 in an external strong magnetic field are evaluated. Furthermore, the two low-lying excited states <img src="Edit_d92f9e9d-e574-4fa3-91fb-a153db020509.png" alt="" /></span><span style="font-family:;" "="">, <span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><img src="data:image/png;base64,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" alt="" /> <img src="Edit_5bf0039b-89f7-4346-a3cb-178f5df359cf.png" width="0" height="0" alt="" /><img src="data:image/png;base64,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" alt="" /><img src="Edit_41f9b122-3fdc-4f01-9470-542944413516.png" alt="" /></span><span style="font-family:;" "="">and <img src="data:image/png;base64,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" alt="" /><span></span></span><span style="font-family:;" "=""><span> <img src="Edit_79f5e8c8-0b24-4dfd-8b9e-080183cc967f.png" alt="" /></span>of the lithium atom in strong magnetic field are also investigated</span><span style="font-family:;" "="">. </span><span style="font-family:;" "="">Simple trial wave functions for lithium are used.</span>
基金The project supported by National Natural Science Foundation of China under Grant No. 10147207, the Natural Science Foundation of Chongqing Science and Technology Committee under Grant No. 2005BB8267, and the Fundamental Research Foundation of Chongqing Education Committee under Grant No. KJ060813
文摘In this study, we show how to generalize Hirshfeld partitioning methods to possibly include non-spherical proatom densities. While this generalization is numerically challenging(requiring global optimization of a large number of parameters), it is conceptually appealing because it allows the proatoms to be pre-polarized, or even promoted, to a state that more closely resembles the atom in a molecule. This method is based on first characterizing the convex set of proatom densities associated with the degenerate ground states of isolated atoms and atomic ions. The preferred orientation of the proatoms' densities are then obtained by minimizing the information–theoretic distance between the promolecular and molecular densities. If contributions from excited states(and not just degenerate ground states) are included in the convex set, this method can describe promoted atoms. While the procedure is intractable in general, if one includes only atomic states that have differing electron-numbers and/or spins, the variational principle becomes a simple convex optimization with a single unique solution.
基金Supported by the National Natural Science Foundation of China under Grant No.11274095the Program of Innovation Scientists and Technicians Troop Construction Projects in Henan Province under Grant No.114100510021+1 种基金the Natural Science Basic Research Plan in Henan Province of China under Grant No.2011B140010the Innovative Research Team(in Science and Technology)in University of Henan Province under Grant No.2010IRTSTHN002
文摘The ground states of the ultracold spin-1 atoms trapped in a deep one-dimensional double-well optical superlattice in a weak magnetic field are obtained. It is shown that the ground-state diagrams of the reduced double- well model are remarkably different for the antiferromagnetic and ferromagnetic condensates. The transition between the singlet state and nematic state is observed for the antiferromagnetic interaction atoms, which can be realized by modulating the tunneling parameter or the quadratic Zeeman energy. An experiment to distinguish the different spin states is suggested.
