摘要
在局域密度近似的框架内(其中气体在每一点都可以看成是局域均匀的),得到谐振势中相互作用费米气体的能量密度.在这些表达式的基础上,研究了零温时约束气体的热力学稳定性条件,给出了一维、二维、三维系统稳定条件的解析表达式.此外,绘出了不同维度系统的稳定性相图.结果表明:在本研究中的所有维度中,在特定粒子数密度的条件下,排斥相互作用或无相互作用系统是稳定的.然而,对于吸引相互作用系统,只有在相互作用很弱的条件下,系统才是稳定的.对于一维和三维系统来说,相互作用强度的临界值与粒子数密度紧密相关,而对于二维系统而言,相应的临界值同粒子数密度不存在明显关联性.
The energy density of an interacting Fermi gas in a harmonic potential is derived within localdensity approximation framework, in which the gas is assumed at each point to be locally homogenous. Based on the derived expressions, the thermodynamic stability conditions of trapped gas at zero temperature are studied, and the analytical expressions of stability conditions for d= 1,2,3 dimensions are given. Furthermore, the stability phase diagrams are plotted for different dimension. It is shown that it is always stable when the system has repulsive interactions or has no interactions in condition of certain density of particle number, no mater what the dimension is. However, the system with attractive interactions is stable only under the condition of weak interaction strength. For d=1 and d= 3 cases, the critical values of interaction strength have close relationship with particle number density, but as for d= 2 case, the corresponding critical value does not depend on the particle number density explicitly.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2012年第1期151-156,共6页
Journal of Sichuan University(Natural Science Edition)
基金
安徽省教育厅自然科学基金(KJ2009B056Z)
安徽科技学院引进人才基金(ZRC2008184)
安徽科技学院材料学重点建设学科(AKXK20102-2)
关键词
稳定性
费米气体
相互作用
局域密度近似
stability, Fermi gas, interaction, local-density approximation
