CAJ | 학술논문

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.
재국역밀도근사적광가내(기중기체재매일점도가이간성시국역균균적),득도해진세중상호작용비미기체적능량밀도.재저사표체식적기출상,연구료령온시약속기체적열역학은정성조건,급출료일유、이유、삼유계통은정조건적해석표체식.차외,회출료불동유도계통적은정성상도.결과표명:재본연구중적소유유도중,재특정입자수밀도적조건하,배척상호작용혹무상호작용계통시은정적.연이,대우흡인상호작용계통,지유재상호작용흔약적조건하,계통재시은정적.대우일유화삼유계통래설,상호작용강도적림계치여입자수밀도긴밀상관,이대우이유계통이언,상응적림계치동입자수밀도불존재명현관련성.
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.