玻色-爱因斯坦凝聚中集体激发的Landau阻尼和频移

项目名称： 玻色-爱因斯坦凝聚中集体激发的Landau阻尼和频移

项目编号： No.10864006

项目类型： 地区科学基金项目

立项/批准年度： 2009

项目学科： 轻工业、手工业

项目作者： 马晓栋

作者单位： 新疆师范大学

项目金额： 25万元

中文摘要： 本项目采用Hartree-Fock-Bogoliubov平均场近似，研究囚禁玻色-爱因斯坦凝聚中集体激发的阻尼和频移. 尽管国际上有很多玻色气体凝聚集体激发阻尼的理论研究，但实验现象没有得到很好的解释.另外频移是是与阻尼相伴的物理现象，但在阻尼的理论研究中没有频移的计算.我们在准一维、准二维排斥相互作用系统Landau阻尼的研究中，指出原来计算阻尼通常方法中的问题，提出了一种考虑元激发实际弛豫的新方法，在系统参量相同的条件下，理论结果与三维实验结果相符.我们在球对称系统的研究中，对前期工作中消除Thomas-Fermi近似发散的解析方法进行了合理的改进，并采用考虑实际弛豫的新方法，理论计算结果与现有的数值模拟计算结果非常接近.我们通过大量的编程计算和理论分析逐渐完成了上述理论上的突破。我们还研究了准一维吸引相互作用系统，推导了三模耦合矩阵元的解析表达式，可以详细讨论系统的性质.我们将进一步解析和数值模拟研究轴对称系统的阻尼，由于考虑实际弛豫的新方法比原来通常方法更合乎物理意义，从而可以给出计算频移的公式，频移比阻尼更依赖于系统的能级结构，因此频移的计算将在有实验研究的轴对称系统中实现.

中文关键词： 玻色-爱因斯坦凝聚；Hartree-Fock-Bogoliubov平均场近似；阻尼和频移；实际弛豫

英文摘要： We investigate the damping and the frequency-shift of the collective mode in trapped Bose-Einstein condensate by using the Hartree-Fock-Bogoliubov approximation. Although there are a lot of studies on the damping of the collective excitation in the trapped Bose-Einstein condensate in the world, the experimental phenomena is not yet very well understood. The frequency-shift is the concomitant phenomenon of the damping, but there is no calculation of the frequency-shift in the study of the damping. By point out the defects in the uasual caculation method, we put forward a new method considering the practical relaxation of the elementary excitation in the study of the Landau damping for the quasi-one-dimension and quasi-two-dimension repulsive system. In the condition of equal system parameters, our theoretic results are in agreement with the experiment ones for three dimensional system. In the study of the spherical, we improving the analytical method in our former work eliminating the divergence of the Thomas-Fermi approximation and use new method considering the practical relaxation. The analytical result is found to be close to the existing numerical simulation result. By means of a good deal of programming calculation and theoretic analysis, we have been improving our new method piece by piece. In studing of the quasi-one-dimension attactive system, we deduce the analytical expression of the three modes coupling matrix element and therefor could carefully discuss the system character. We are going to study the damping of the axial system with analytical and numerical simulatio method. As the method considering the practical relaxation is more reasonable than the uasual method, the calculation fomula of the frequency-shift is available. As the frequency-shift is much more dependents on the energy level structure of the system, the calculation of the frequency-shift will be realized in the study of the axial system which phenomena is observed in experiment.

英文关键词： Bose-Einstein condensate; damping and frequency-shift; Hartree-Fock-Bogoliubov approximation; practical relaxation