一维硬壁分裂势中少玻色子系统的基态性质
Ground-state properties of few-Boson system in a one-dimensional hard wall potential with split
摘要：
本文详细研究了中心有$δ-$分裂的一维硬壁势中少玻色子系统的基态性质。在Tonks-Girardeau极限下，粒子间具有无穷大的排斥力，我们利用玻色-费米映射构造了精确的$N-$粒子基态波函数，使我们能够精确地研究关联性质.对于一般的有限粒子间相互作用情形，利用精确对角化方法研究了不同相互作用强度和势垒高度下的基态密度分布、占据数分布和动量分布.动量分布中的次峰揭示了分裂两侧粒子间的干涉，这种干涉在势垒强度大、相互作用强度小的情况下更为突出。
英文摘要：
We carry out a detailed examination of the ground state property of few-boson system in a one-dimensional hard wall potential with a $δ-$ split in the center. In the Tonks-Girardeau limit with infinite repulsion between particles, we use the Bose-Fermi mapping to construct the exact $N-$ particle ground state wavefunction which allows us to study the correlation properties accurately. For the general case with finite inter-particle interaction, the exact diagonalization method is exploited to study the ground-state density distribution, occupation number distribution, and momentum distribution for variable interaction strengths and barrier heights. The secondary peaks in the momentum distribution reveal the interference between particles on the two sides of the split, which is more prominent for large barrier strength and small interaction strength.
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