The ground-state properties of a system with a small number of interacting bosons over a wide range of densities are investigated. The system is confined in a two-dimensional isotropic harmonic trap, where the interac...The ground-state properties of a system with a small number of interacting bosons over a wide range of densities are investigated. The system is confined in a two-dimensional isotropic harmonic trap, where the interaction between bosons is treated as a hard-core potential. By using variational Monte Carlo method, we diagonalize the one-body density matrix of the system to obtain the ground-state energy, condensate wavefunction and the condensate fraction. We find that in the dilute limit the depletion of central condensate in the 2D system is larger than in a 3D system for the same interaction strength; however as the density increases, the depletion at the centre of 2D trap will be equal to or even lower than that at the centre of 3D trap, which is in agreement with the anticipated in Thomas-Fermi approximation. In addition, in the 2D system the total condensate depletion is still larger than in a 3D system for the same scattering length.展开更多
In <span style="font-family:;" "="">the <span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of the lithium ...In <span style="font-family:;" "="">the <span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of the lithium atom and l<span style="font-family:;" "="">ithium like ions up to Z = 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 style="font-family:;" "="">, <span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><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 style="font-family:;" "="">and <img src="data:image/png;base64,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" alt="" /><span style="font-family:;" "=""> <img src="Edit_79f5e8c8-0b24-4dfd-8b9e-080183cc967f.png" alt="" />of the lithium atom in strong magnetic field are also investigated<span style="font-family:;" "="">. <span style="font-family:;" "="">Simple trial wave functions for lithium are used.展开更多
In Bayesian multi-target fltering,knowledge of measurement noise variance is very important.Signifcant mismatches in noise parameters will result in biased estimates.In this paper,a new particle flter for a probabilit...In Bayesian multi-target fltering,knowledge of measurement noise variance is very important.Signifcant mismatches in noise parameters will result in biased estimates.In this paper,a new particle flter for a probability hypothesis density（PHD）flter handling unknown measurement noise variances is proposed.The approach is based on marginalizing the unknown parameters out of the posterior distribution by using variational Bayesian（VB）methods.Moreover,the sequential Monte Carlo method is used to approximate the posterior intensity considering non-linear and non-Gaussian conditions.Unlike other particle flters for this challenging class of PHD flters,the proposed method can adaptively learn the unknown and time-varying noise variances while fltering.Simulation results show that the proposed method improves estimation accuracy in terms of both the number of targets and their states.展开更多
文摘The ground-state properties of a system with a small number of interacting bosons over a wide range of densities are investigated. The system is confined in a two-dimensional isotropic harmonic trap, where the interaction between bosons is treated as a hard-core potential. By using variational Monte Carlo method, we diagonalize the one-body density matrix of the system to obtain the ground-state energy, condensate wavefunction and the condensate fraction. We find that in the dilute limit the depletion of central condensate in the 2D system is larger than in a 3D system for the same interaction strength; however as the density increases, the depletion at the centre of 2D trap will be equal to or even lower than that at the centre of 3D trap, which is in agreement with the anticipated in Thomas-Fermi approximation. In addition, in the 2D system the total condensate depletion is still larger than in a 3D system for the same scattering length.
文摘In <span style="font-family:;" "="">the <span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of the lithium atom and l<span style="font-family:;" "="">ithium like ions up to Z = 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 style="font-family:;" "="">, <span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><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 style="font-family:;" "="">and <img src="data:image/png;base64,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" alt="" /><span style="font-family:;" "=""> <img src="Edit_79f5e8c8-0b24-4dfd-8b9e-080183cc967f.png" alt="" />of the lithium atom in strong magnetic field are also investigated<span style="font-family:;" "="">. <span style="font-family:;" "="">Simple trial wave functions for lithium are used.
基金supported by National High-tech Research and Development Program of China (No.2011AA7014061)
文摘In Bayesian multi-target fltering,knowledge of measurement noise variance is very important.Signifcant mismatches in noise parameters will result in biased estimates.In this paper,a new particle flter for a probability hypothesis density（PHD）flter handling unknown measurement noise variances is proposed.The approach is based on marginalizing the unknown parameters out of the posterior distribution by using variational Bayesian（VB）methods.Moreover,the sequential Monte Carlo method is used to approximate the posterior intensity considering non-linear and non-Gaussian conditions.Unlike other particle flters for this challenging class of PHD flters,the proposed method can adaptively learn the unknown and time-varying noise variances while fltering.Simulation results show that the proposed method improves estimation accuracy in terms of both the number of targets and their states.
