A simple and direct approach to handle summation is presented. With this approach, we analytically investigate Bose–Einstein condensation of ideal Bose gas trapped in an isotropic harmonic oscillator potential. We ge...A simple and direct approach to handle summation is presented. With this approach, we analytically investigate Bose–Einstein condensation of ideal Bose gas trapped in an isotropic harmonic oscillator potential. We get the accurate expression of which is very close to (0.43% larger than) the experimental data. We find the curve of internal energy of the system vs. temperature has a turning point which marks the beginning of a condensation. We also find that there exists specific heat jump at the transition temperature, no matter whether the system is macroscopic or finite. This phenomenon could be a manifestation of a phase transition in finite systems.展开更多
A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresp...A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresponding ideal gas. We obtain the expression of the transition temperature shift as , where n is the density of particle number and a is the scattering length. The result has never been reported in the literature.展开更多
基金国家自然科学基金，the Chinese Foundation of High Education
文摘A simple and direct approach to handle summation is presented. With this approach, we analytically investigate Bose–Einstein condensation of ideal Bose gas trapped in an isotropic harmonic oscillator potential. We get the accurate expression of which is very close to (0.43% larger than) the experimental data. We find the curve of internal energy of the system vs. temperature has a turning point which marks the beginning of a condensation. We also find that there exists specific heat jump at the transition temperature, no matter whether the system is macroscopic or finite. This phenomenon could be a manifestation of a phase transition in finite systems.
文摘A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresponding ideal gas. We obtain the expression of the transition temperature shift as , where n is the density of particle number and a is the scattering length. The result has never been reported in the literature.
