有限尺度下弱相互作用费米气体的热力学性质

基于巨正则系综理论和数值模拟方法,研究有限尺度下弱相互作用费米气体的热力学性质,给出系统低温下的化学势、能量及热容量的解析式,分析弱相互作用、有限尺度效应对系统热力学性质的影响.研究表明,有限尺度和排斥相互作用增大了系统的化学势、能量,吸引相互作用减小了系统的化学势、能量.相互作用受到尺度的调制,尺度变大,相互作用影响变小,相互作用和尺度效应都受到温度的调制,温度升高,相互作用和尺度的影响减小.尺度和相互作用的一级修正对热容量无影响.

Thermodynamic properties of weakly interacting Fermi gas in finite size space

Based on quantum statistical grand canonical ensemble theory and the methods of numerical simulation, taking into account the weak interaction between the particles, we studied the thermodynamic properties of Fermi gas in finite-size space, gave the analytic expressions of Chemical potential, energy and heat capacity, analyzed the weak interaction, finite size effects on the thermodynamic properties of the system. The results showed finite-size effects and repulsive interactions increase the system's chemical potential, energy, attractive interaction decrease the system's chemical potential, energy. Interaction was modulated by the finite size effects, the size larger, the interaction effects smaller. Interaction, and finite-size effects are all modulated by temperature, with the temperature rising, The impact of interaction and finite-size effects reducing. Considering the first-order correction of interaction and finite-size effects, they had no effect on the heat capacity.