反常磁矩对弱磁场弱相互作用费米气体热力学性质的影响

考虑费米子的反常磁矩, 运用赝势法和热力学理论, 导出弱磁场中弱相互作用费米气体自由能的解析式, 以此为基础给出高温和低温情况下系统热力学性质, 分析反常磁矩对热力学性质的影响机理. 研究表明: 反常磁矩对热力学性质的影响与温度相关, 而且这种影响随温度的上升在低温区是增大的, 在高温区是减小的; 对于系统的化学势、内能, 反常磁矩加强了磁场的影响, 弱化了相互作用的影响; 对于系统的热容量, 反常磁矩在低温区使其减小, 在高温区使其增加.     

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.     

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     

磁场中非广延相对论费米系统的统计性质

基于广义外势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热力学性质,给出总能、热容量、化学势的解析式,分析非广延参数、极端相对论效应、磁场及温度对系统热力学性质的影响机理.研究显示,非广延参数不仅对热力学性质有直接的影响,而且也影响着磁场的物理效应. 随温度的升高,非广延参数及磁场对热力学性质的影响均被放大.极端相对论效应对化学势及热容量有特别显著的影响.     

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     

Statistic properties of Fermi gas in a strong magnetic field

Based on the thermodynamic potential function of Fermi gas in a strong magnetic field, using the thermodynamics method, the integrated analytical expressions of thermodynamic quantities of the system at low temperatures are derived, and the effects of the magnetic field on the statistic properties of the system are analysed. It is shown that, as long as the temperature is not zero, the effects of the magnetic field on the thermodynamic quantities of the system contain both oscillatory and non-oscillatory parts. For the non-oscillatory part, compared with the situation of Fermi gas in a weak magnetic field, the influence of the magnetic field on the thermodynamic quantities is not exactly the same. For the oscillatory part, the period and amplitude of the oscillation are all related to the magnetic field. Due to the oscillation, the chemical potential may be greater than Ferim energy of the system, but the oscillation does not affect the thermodynamic stability of the system.     

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     

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.     

基于准经典近似研究强磁场中高温费米气体的统计性质

基于准经典近似研究强磁场中高温费米气体的统计性质,给出系统的统计特征量的解析式,分析磁场和温度对统计性质的影响.结果显示,与低温情况比较,高温下的统计特征量不再振荡,与自由费米气体比较,磁场总是降低系统的总能,增加系统的化学势、热容量、熵、压强和稳定性;而且温度越高,磁场对总能及热容量的影响越弱,对化学势的影响越大.     

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.     

Heat capacity and entropy of two electrons quantum dot in a magnetic field with parabolic interaction

The thermodynamic properties of two electrons in two dimensional parabolic GaAs quantum dot are studied where both the magnetic field and the e–e interaction are fully considered. The e–e interaction has been treated by a model potential which makes the Hamiltonian exactly solvable. The energy spectrum is used to calculate the canonical partition function, and then we obtain the thermodynamic properties; mean energy, heat capacity and entropy as a function of temperature (T) and magnetic field (B).A steep transition from zero to 4k_B is observed in the heat capacity as a function of temperature for small values of magnetic field and saturates within a small temperature range, also the heat capacity has a peak-like structure at low temperature, while for high magnetic field heat capacity develops a shoulder at 2k_B then it approaches the saturation value with further increase in temperature. The entropy increases with increasing temperature, but at higher temperature, it remains almost independent of the magnetic field. It is shown that, at low magnetic field values, the effect of magnetic field on heat capacity is tangible and it attains a constant value with further increase in magnetic field. Entropy is almost linearly proportional with increasing magnetic field strength.     

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。     

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     

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.     

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.     

自旋与手征动力学的输运模拟研究

自旋相关的物理是多个研究领域的热门课题。核子和夸克都是自旋为1/2的费米子,在非对心重离子碰撞中受到自旋-轨道相互作用以及磁场的影响,会产生有趣的自旋动力学,特别是在垂直于反应平面方向上会出现自旋极化。在相对论重离子碰撞中,由于产生了极端的高温高密环境,夸克可以近似看作无质量粒子,此时自旋动力学过渡为手征动力学。在外界电磁场、涡旋场作用下以及在电荷与手征荷不对称的条件下,会产生一系列手征反常效应。本文介绍我们课题组基于输运模拟在自旋与手征动力学方面开展的一系列研究工作,包括中能重离子碰撞及相对论重离子碰撞中粒子的自旋极化、理想体系及相对论重离子碰撞中的手征磁波等。     

A Monte Carlo study of the thermodynamic properties of a quasi-one-dimensional organic polymer ferromagnet

The thermodynamic properties of a quasi-one-dimensional organic ferromagnet at different temperatures and in different applied magnetic fields have been investigated by means of the Heisenberg model combined with the Monte Carlo method. The results indicate that a peak in the magnetic susceptibility is obtained at low temperatures. Furthermore, the effect of dimerization on the magnetic properties has also been studied. We find that the dimerization suppresses the magnetization in this model. The ferromagnetic couplings between the side-free radicals stabilize the ferromagnetism and increase the apparent Curie temperature.     

耦合电磁场对石墨烯量子磁振荡的影响

我们研究了包含自旋轨道耦合与杂质散射在内的石墨烯量子磁振荡对外加电磁场的响应.我们发现,石墨烯中自旋轨道耦合、电磁场以及边界共同修正了朗道能谱,且当电场与磁场比值超过某一临界值时,量子磁振荡会突然消失,这与非相对论二维电子气的情况显著不同.这种现象可以通过朗道量子化轨道由封闭转化为开放的半经典理论来解释.此外,我们还发现杂质散射和温度的共同作用会使得磁振荡振幅衰减.我们的结果可用于分析石墨烯及其类似结构(硅烯、锗烯、锡烯等)的费米能级与朗道能谱的相互作用,进而探测自旋轨道耦合引起的能隙.     

重力场和强磁场中费米气体的热力学性质

基于半经典近似,研究重力场和强磁场共存下费米气体的热力学性质,通过理论解析和数值模拟分析强磁场背景下重力场对系统热力学性质的影响.研究表明:与单纯强磁场相比,重力场的引入使能量及化学势都降低.随温度的上升,重力场对化学势的影响逐渐放大;对热容的影响有极大值.重力场使系统的热容随磁场的振荡几乎不变、使化学势的振荡中心下移.     

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.