一维强相互作用的玻色-费米混合气体关联特性研究

Correlation properties of Bose⁃Fermi mixture with one-dimensional strong interaction

详细分析了一维强相互作用的玻色-费米混合气体的空间关联特性,重点讨论了在绝对零度和有限低温下处于Tonks-Girardeau原子气区域的玻色-费米混合量子气体的两体空间关联函数,并将复杂难算的多体波函数的空间关联函数转化为容易计算的矩阵行列式。研究结果表明,绝对零度下对于固定数目的玻色子(费米子),费米子(玻色子)的数目对玻色子(费米子)空间关联函数图样影响不大;而有限温度下,费米子(玻色子)的数目对玻色子(费米子)空间关联函数影响较大,且随着温度的提升,另一种粒子的数目对关联结果的影响也更显著。此外,当总粒子数目一定时,无论是在绝对零度还是有限低温下,相同数目的玻色子和费米子的关联结果一致。

The spatial two-body correlations of Bose-Fermi mixture with equal masses of bosons and fermions in Tonks-Girardeau regime under periodic boundary conditions are theoretically investigated.Combining the exact solution of the quantum many-body system,the analytical formula of the spatial correlation functions for Bose-Fermi mixture at both absolute zero temperature and finite low temperatures are derived using some calculating techniques.The results show that,for a fixed number of bosons(fermions)at absolute zero temperature,the number of fermions(bosons)has little effect on the spatial correlation function of bosons(fermions).By contrast,at finite temperature,the number of fermions(bosons)has a greater effect on the spatial correlation function of bosons(fermions),and with the increase of temperature,the influence of the other particles number on the correlation results will be more significant.In addition,when the total particle number is fixed,the correlation results of the same number of bosons and fermions are consistent whether at absolute zero temperature or at a finite temperature.