弱相互作用费米气体的热力学性质

根据赝势法导出无外势时弱相互作用费米气体的化学势、内能和定容热容的解析表达式.在此基础上，采用局域密度近似研究谐振势中弱相互作用费米气体的热力学性质，探讨粒子间相互作用对系统性质的影响. 关键词： 费米气体 相互作用 赝势法 局域密度近似 热力学性质     

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.     

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     

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     

由N-E-V分布及赝势法研究弱磁场中弱相互作用费米子气体的热力学性质

基于低温下量子系统的相关实验多是在体积、能量和粒子数都可变的外场束缚下进行的事实, 由体积、能量和粒子数可变的完全开放系统的统计分布(N-E-V分布)研究了弱磁场中弱相互作用费米系统的热力学性质. 首先求出了一般情况下由费米积分表示的内能和热容的解析表达式. 在此基础上, 又给出了在低温极限条件下内能与热容的解析表达式和数值计算结果, 并将N-E-V分布(粒子数密度变化)的结果与赝势法(粒子数密度不变)的结果进行了比较. 结果表明: N-E-V分布方法的计算结果总是补偿赝势法计算结果的过度偏差. 由N-E-V 分布方法所得结果最特异之处在于: 在低温条件下, 弱磁场中弱相互作用费米系统存在一相变温度t_c, 其正处于费米系统发生玻色-爱因斯坦凝聚(BEC)和费米原子形成库珀对的超流状态(BCS)相变及BEC-BCS跨越的温度范围内, 且不随反映弱相互作用大小和特征的散射长度a (a<0引力, a>0斥力)变化, 但随弱磁场的加强而降低, 即弱磁场可调节该相变温度. 磁场为零时, 相变温度最高, 为费米温度的0.184倍.     

实际费米气体的低温性质

实际气体粒子间都存在弱的相互作用,利用赝势法求出无外势时实际费米气体的能谱,导出了低温低密度下实际费米气体的化学势、压强、熵、内能和定容热容等物理量的解析表达式,探讨了粒子间相互作用对系统低温性质的影响．     

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.     

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.     

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.     

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     

Chemical pressure effect on the superconductor MgCNi3

In order to investigate the positive and negative pressure effects on superconducting properties for MgCNi₃, chemical pressure was applied by means of Zn-doping to Mg site (Mg_1−xZn_xCNi₃) and by substituting Mg with Cd (CdCNi₃). The lattice constant decreases (increases) with increasing Zn (Cd) content. In the magnetic measurements, superconducting transition temperature (T_c) is decreasing with increasing Zn content and disappears at x > 0.3. While for CdCNi₃, T_c also decreases down to 3.4 K. The result seems not to be fully understandable in the case of CdCNi₃ since T_c seems to rise owing to the increase of density of states at Fermi energy caused by lattice expansion.     

The universal sound velocity formula for the strongly interacting unitary Fermi gas

Due to the scale invariance,the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas.For example,the virial theorem between pressure and energy density of the ideal gas P=2E/3V is still satisfied by the unitary Fermi gas.This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation.For comparison,the sound velocities for the ideal Boltzmann,Bose and Fermi gas are also given.Quite interestingly,the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions.     

Entropy of the rotating and charged black string to all orders in the Planck length

<正>By using the entanglement entropy method,this paper calculates the statistical entropy of the Bose and Fermi fields in thin films,and derives the Bekenstein-Hawking entropy and its correction term on the background of a rotating and charged black string.Here,the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string.Taking into account the effect of the generalized uncertainty principle on quantum state density,it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model.These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect.The ultraviolet cut-off in the brick-wall model is not reasonable.The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon.From the viewpoint of quantum statistical mechanics,the correction value of Bekenstein-Hawking entropy is obtained.This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates.     

磁性纳米颗粒系统偶极相互作用的Monte Carlo研究

采用局域Monte Carlo方法模拟不同易轴分布的简单立方排列单分散单畴Fe纳米颗粒系统的ZFC-FC曲线及磁滞回线.结果表明：随着偶极相互作用的增强，系统的阻塞温度T_B逐渐增大，且ZFC曲线的峰变宽.说明偶极相互作用使得系统的有效能垒提高，分布宽度增加.研究FC曲线磁化强度的倒数与温度关系，发现偶极相互作用系统中存在反铁磁有序.系统的阻塞态及超顺磁态的磁滞回线表明，极低低温下，随着偶极相互作用的增强，系统的矫顽力和剩磁减小，偶极相互作用阻碍系统的磁化；系统处于超顺磁态，各向异性作用及偶极相互作用使得系统的磁化曲线偏离Langevin曲线且偶极相互作用展现出退磁相互作用效应.偶极相互作用增强，系统磁化曲线与Langevin曲线偏差量的最大值向低场移动.在偶极相互作用下，易轴与外场夹角为45°的磁性纳米颗粒系统的平均有效能垒和有效能垒分布宽度较易轴随机分布系统的大.     

Generalized uncertainty principle and black hole entropy

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein–Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this Letter, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty principle and obtain the correction terms of entropy, temperature and energy caused by the generalized uncertainty principle. We calculate Cardy–Verlinde formula after considering the correction. In our calculation, we only think that the Bekenstein–Hawking area theorem is still valid after considering the generalized uncertainty principle and do not introduce any assumption. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the corrections caused by the generalized uncertainty principle to the black hole thermodynamic quantity of the complicated spacetime.     

Composite-fermionization of the mixture composed of Tonks gas and Fermi gas

This paper investigates the ground-state properties of the mixture composed of the strongly interacting Tonks-Girardeau gas and spin polarized Fermi gas confined in one-dimensional harmonic traps, where the interaction between the Bose atoms and Fermi atoms is tunable. With a generalized Bose-Fermi transformation the mixture is mapped into a two-component Fermi gas. The homogeneous Fermi gas is exactly solvable by the Bethe-ansatz method and the ground state energy density can be obtained. Combining the ground-state energy function of the homogeneous system with local density approximation it obtains the ground-state density distributions of inhomogeneous mixture. It is shown that with the increase in boson-fermion interaction, the system exhibits composite-fermionization crossover.     

Surface electron doping induced double gap opening in Td-WTe2

By using scanning tunneling microscopy, we investigated the electronic evolution of T_d-WTe₂ via in-situ surface alkali K atoms deposition. The T_d-WTe₂ surface is electron doped upon K deposition, and as the K coverage increases, two gaps are sequentially opened near Fermi energy, which probably indicates that two phase transitions concomitantly occur during electron doping. The two gaps both show a dome-like dependence on the K coverage. While the bigger gap shows no prominent dependence on the magnetic field, the smaller one can be well suppressed and thus possibly corresponds to the superconducting transition. This work indicates that T_d-WTe₂ exhibits rich quantum states closely related to the carrier concentration.     

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.