论文摘要
在实验上,Feshbach共振原理、磁光阱束缚以及原子芯片的应用技术日渐成熟,实现了制备准一维玻色爱因斯坦凝聚,并且对冷原子的研究已经从单分量气体扩展到玻色费米混合物或是两分量玻色气体混合物等领域。在多体量子系统中,低维系统受到物理学家的关注,体系维数降低时,就会增强粒子间相互作用与量子涨落和关联。Bethe-Ansatz方法的优点在于给出了多粒子系统在任何相互作用强度下都满足的精确解方程。推广到热力学范围,热力学Bethe-Ansatz方程的结果和实验结论也是一致的。因此在诸多模型中,Bethe-Ansatz方法就成为理论研究的重要手段,并且给出了很多有意义的结果。在理论上,一维多体量子系统处理起来相对比较简单,而且有可能找到其精确解析解。本文简单介绍了开边界和周期边界条件下的Bethe-Ansatz方程。主要计算了在开边界条件下,一维δ相互作用玻色子在排斥和吸引相互作用下的Bethe-Ansatz方程,重点讨论了三个典型的量子相的能谱、单体密度矩阵分布和关联函数。在相图里有两个临界点,Tonks-Girardeau （TG）气体和super Tonks-Girardeau （STG）气体在强相互作用极限-1/γ=0有相同的性质；然而在弱相互作用极限γ=0附近,可以从排斥相互作用的基态（TG）平滑地过渡到吸引相互作用的基态（BS）。另外,基于一维量子气体的Lieb-Liniger模型,从玻色费米混合物的热力学Bethe-Ansatz方程出发,通过迭代求解的方法,我们得到了系统在强相互作用情况下的基态能量解,并和数值解进行了比较分析。
论文目录
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