强磁场中相互作用费米气体的相对论稳定性

由单粒子的弱相互作用能谱及泊松公式,导出了强磁场中相互作用费米气体的相对论热力学势函数,求解了系统力学稳定性的判别式,分析了相互作用、磁场及相对论效应对系统稳定性的影响机理。结果表明,强磁场中弱相互作用费米气体的力学稳定性会受到弱相互作用的影响,强磁场对这种影响具有调节作用,而相对论效应对相互作用的影响基本没有调节作用。     

强磁场中超冷费米气体的相对论效应

由单粒子的弱相对论能谱及泊松公式,导出强磁场中费米气体的热力学势函数.在此基础上,运用热力学关系求解低温条件下系统的统计特征量的解析式,分析相对论效应对统计性质的影响机理.研究表明,磁场愈强,相对论效应愈明显.相对论效应引发的单调项与相应的振荡项的振幅相比,对总能,单调项远大于振幅;对化学势及磁矩,单调项与振幅几乎同一量级. 关键词： 强磁场 费米气体 相对论效应     

弱相互作用费米气体的相对论顺磁性

通过考虑单粒子的相对论能量并且应用量子统计方法,研究弱磁场中弱相互作用费米气体的相对论顺磁性,求解相对论性的最可几磁化率及平均磁化率,讨论相对论效应对最可几磁化率的影响,给出相对论性的粒子数的临界值. 结果显示, 与非相对论情况比较,当 时, 相对论情况下的最可几磁化率和粒子数的临界值都没有变化. 当 时,相对论效应使系统呈现顺磁性容易,而且相对论效应增加磁化率,同时也放大了相互作用对磁化率的影响.     

弱相互作用费米气体的相对论顺磁性

通过考虑单粒子的相对论能量并且应用量子统计方法，研究弱磁场中弱相互作用费米气体的相对论顺磁性，求解相对论性的最可几磁化率及平均磁化率，讨论相对论效应对最可几磁化率的影响，给出相对论性的粒子数的临界值. 结果显示, 与非相对论情况比较，当 时, 相对论情况下的最可几磁化率和粒子数的临界值都没有变化. 当 时，相对论效应使系统呈现顺磁性容易，而且相对论效应增加磁化率，同时也放大了相互作用对磁化率的影响.     

强磁场中弱相互作用费米气体的热力学性质

基于赝势法和局域密度近似研究了强磁场中弱相互作用费米气体的热力学性质,得出化学势、总能和热容量的解析式,同时分析了磁场及相互作用对系统热力学性质的影响.研究表明,无论是高温情况还是低温情况下,磁场都能调节相互作用的影响.低温下,与无磁场的系统相比,磁场降低系统的化学势、总能和热容量;与无相互作用系统相比,排斥作用增加化学势而降低总能及热容量.高温下,磁场和排斥作用均可降低系统的总能而增加热容量,强磁场可以改变相互作用对总能及热容量的影响. 关键词： 强磁场 弱相互作用 费米气体 热力学性质     

磁场中非广延相对论费米系统的稳定性

基于磁场中的非广延统计理论,运用理论解析与数值模拟方法,研究磁场中非广延极端相对论费米气体的力学稳定性,给出高温与低温下稳定性条件的解析式,分析非广延参数、极端相对论效应、磁场及温度对系统稳定性的影响机理.     

弱相互作用费米气体的不稳定性判据

根据由赝势法得到的弱相互作用费米气体的自由能，利用热力学方法研究了无外场时弱相互作用费米气体的稳定性.结果表明，无外场情况下理想费米气体与存在弱排斥相互作用的费米气体是稳定的；而具有弱吸引相互作用的费米气体在一定条件下可出现不稳定性.给出了不稳定性的粒子数密度判据和温度判据，就不同逸度情况下临界粒子数密度的具体表达结果以及温度、粒子质量和吸引相互作用对临界粒子数密度的影响进行了讨论. 关键词： 费米气体 相互作用 不稳定性判据     

磁场中非广延相对论费米系统的稳定性

基于磁场中的非广延统计理论,运用理论解析与数值模拟方法,研究磁场中非广延极端相对论费米气体的力学稳定性,给出高温与低温下稳定性条件的解析式,分析非广延参数、极端相对论效应、磁场及温度对系统稳定性的影响机理     

弱磁场中弱相互作用费米气体的热力学性质

根据赝势法和系综理论导出弱磁场中弱相互作用费米气体的内能、化学势和热容量的小参数r的解析式.在此基础上给出高温和低温两种情况下弱磁场中弱相互作用费米气体的热力学性质,探讨磁场及粒子间相互作用对热力学性质的影响,分析磁场与三维谐振势两种约束对系统性质影响的不同及其原因. 关键词： 赝势法 费米气体 相互作用 热力学性质     

硬球势中相对论费米气体的热力学性质

用量子统计与数值模拟相结合的方法,在广义外势中相对论费米系统的热力学量的基础上,研究硬球势中相对论费米气体的热力学性质.得到了考虑相对论效应时系统的内能和热容量的解析表达式,分析了相对论效应对内能和热容量的影响.研究表明:与非相对论比较,相对论费米气体的内能和热容量更高;相对论特征量越大,热容量的转折温度越低;随着温度的升高,特征量越大,内能就越大.     

Relativity stability of quantum gas in a weak magnetic field

Based on the analytical expression of relativistic free energy for a weakly interacting Fermi gas in a weak magnetic field,by using the method of quantum statistics,the stability conditions of the system at both high and low temperatures are given,and the effects of magnetic field and interparticle interactions on the stability of the system are analysed.It is shown that at high temperatures,the stability conditions of the system are completely the same,no matter whether it is the ultrarelativistic case or nonrelativistic case.At extremely low temperatures,the mechanical stability conditions of the system show a similar rule through a comparison between the ultrarelativistic case and nonrelativistic case.At the same time,thermal stability of a relativistic Bose gas in a weak magnetic field is discussed,and the influence of the effect of relativity on the thermal stability of the system is investigated.     

Relativistic thermodynamic properties of a weakly interacting Fermi gas in a weak magnetic field

This paper derives the analytical expression of free energy for a weakly interacting Fermi gas in a weak magnetic field,by using the methods of quantum statistics as well as considering the relativistic effect.Based on the derived expression,the thermodynamic properties of the system at both high and low temperatures are given and the relativistic effect on the properties of the system is discussed.It shows that,in comparison with a nonrelativistic situation,the relativistic effect changes the influence of temperature on the thermodynamic properties of the system at high temperatures,and changes the influence of particle-number density on them at extremely low temperature.But the relativistic effect does not change the influence of the magnetic field and inter-particle interactions on the thermodynamic properties of the system at both high and extremely low temperatures.     

弱磁场中弱相互作用费米气体的有限粒子数效应(英文)

由弱磁场中弱相互作用费米气体的配分函数,导出有限粒子数条件下系统的配分函数G(β,N ).在此基础上,运用统计平均方法求解有限粒子数弱相互作用费米气体热力学量的解析表达式,给出各种温度条件下的热力学性质.研究结果表明,有限粒子数效应使各个热力学量都产生了一个修正项,除温度趋于0外,粒子数对化学势的修正项有直接影响,对内能和热容量的修正项并不产生直接影响.并且有限粒子数效应总是降低化学势,从而使化学势的0点向低温漂移,粒子数增大,会削弱这种效应,粒子间的相互排斥会加强这种效应.     

Unified properties of a weakly interacting Fermi gas in a weak magnetic field

When the orbital motion and the spin motion of particles were considered simultaneously, the thermodynamic potential function of a weakly interacting Fermi gas in a weak magnetic field was derived using the thermodynamics method. Based on the derived expression, the analytical expressions of energy, heat capacity, chemical potential, susceptibility and stability conditions of the system were given, and the effects of the interparticle interactions as well as the magnetic field on the properties of the system were analyzed. It was shown that the magnetic field always causes energy and stability to decrease, while the chemical potential of the system to increase. The repulsive (attractive) interactions always increase (decrease) energy and stability, but decrease (increase) the chemical potential and paramagnetism. The repulsive (attractive) interactions decrease (increase) heat capacity of the system at high temperatures but increase (decrease) it at low temperatures.     

The instability conditions of a gas trapped in weak weakly interacting Fermi magnetic field

In this paper the analytical expression of free energy expressed by small parameter r of a weakly interacting Fermi gas trapped in weak magnetic field is derived by using `the maximum approximation' method and the ensemble theory. Based on the derived expression, the exact instability conditions of a weakly interacting Fermi gas trapped in weak magnetic field at both high and low temperatures are given. From the instability conditions we get the following two results. (1) At the whole low-temperature extent, whether the interactions are repulsive or attractive with (ɑn + 4\varepsilon_F/3) (n and \varepsilon _F denote the particle-number density and the Fermi energy respectively, ɑ= 4π a\hbar_F/ m, and a is s-wave scattering length) positive, there is a lower-limit magnetic field of instability; in addition, there is an upper-limit magnetic field for the system of attractive interactions with (ɑ n + \varepsilon_F/3) negative. (2) At the whole high-temperature extent, the system with repulsive interactions is always stable, but for the system with attractive interactions, the greater the scattering length of attractive interactions | a | is, the stronger the magnetic field is and the larger the particle-number density is, the bigger the possibility of instability in the system will be.