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     

广义不确定性原理下费米气体低温热力学性质

在考虑到广义不确定性原理时, 统计物理中的态密度必须做出修正, 这导致对传统统计物理的所有结果都有不同程度的修正. 在高能、高温条件下, 此修正是颠覆传统观念的, 在低温条件下, 也有一定的修正. 研究了低温条件下考虑到广义不确定性原理时, 理想费米气体和具有弱相互作用费米气体的热力学性质, 分别给出理想费米气体和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, 并以铜电子气体为例进行了具体数值计算, 将计算结果与不考虑广义不确定性原理时的费米气体的热力学性质进行了比较, 探讨了广义不确定性原理对系统热力学性质的影响. 考虑到广义不确定性原理后费米气体的化学势、费米能和基态能增大, 热容减少, 内能随温度的增加先增大, 到某一温度(对于铜电子气体, T/T_F0～0.3)时, 增值为零, 温度再增加内能减少. 这些修正的具体数值主要由粒子数密度决定, 粒子数密度越大, 修正越大.     

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     

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     

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.     

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．     

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     

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.     

强磁场中弱相互作用费米气体的稳定性

运用量子统计理论,研究强磁场中弱相互作用费米系统的稳定性,给出系统稳定性条件的解析式,分析相互作用、磁场对稳定性的影响机制.研究显示:排斥相互作用会增大系统稳定时的化学势,也会增大系统稳定时的空间区域;而加强磁场会减小系统稳定时的空间区域,也会降低系统的粒子数密度分布的稳定性.     

单模光腔中N个二能级原子系统的有限温度特性和相变

本文研究单模光场中N个二能级原子Dicke模型的有限温度特性和相变. 把原子赝自旋转换为双模费米算符, 用虚时路径积分方法推导出系统的配分函数, 对作用量变分求极值得到系统的热力学平衡方程, 及原子布居数期待值和平均光子数随原子-光场耦合强度变化的解析表达式. 重点研究了在量子涨落起主导作用的低温区, 由耦合强度变化产生的从正常相到超辐射相的相变, 指出该相变遵从Landau连续相变理论, 平均光子数可作为序参数, 零值表示正常相, 大于零则为超辐射相. 在零温极限下本文的结果和量子相变理论完全符合. 另外, 本文也讨论了系统的热力学性质, 比较有限温度相变和量子相变的异同. 发现, 在强耦合区低温稳定态的光子数和平均能量都和绝对零度的值趋于一致, 而超辐射相的熵则随耦合强度的增强迅速衰减为零.     

Large N phase transition in the heat kernel on the U (N) group

The large N phase transition point is investigated in the heat kernel on the U(N) group with respect to arbitrary boundary conditions. A simple functional relation is found relating the density of eigenvalues of the boundary field to the saddle point shape of the typical Young tableaux in the large N limit of the character expansion of the heat kernel. Both strong coupling and weak coupling phases are investigated for some particular cases of the boundary holonomy.     

Magnetic phase transition in CsVF4

Magnetization and specific heat measurements are reported on the quasi two-dimensional antiferromagnet CsVF₄. Diverging magnetic susceptibility and specific heat at the Néel temperature are observed in a weak field along the crystallographic c-direction, but with increasing field they are progressively smeared. A hysteresis is observed in dc magnetization below the temperature at which M/H reaches a maximum. We present a possible explanation for these phase transition phenomena from the point of view that this compound is composed of two crystallographically inequivalent magnetic sites.     

Layer dependence of the superconducting transition temperature of HgBa2Can−1CunO2n+2+δ

High-pressure methods have been used to synthesize multiphase compositions in the Hg---12{n−1}n homologous series. The phase assemblages were examined by optical, electron diffraction and X-ray diffraction techniques, and their stoichiometries verified by electron microprobe. Transport and magnetic susceptibility measurements were combined with the results of the phase analysis to establish superconducting transition temperatures for both as-prepared and O₂- or Ar-annealed materials. It was found that the transition temperature peaks at T_c = 134 K for N = 3 and then decreases abruptly for n>4, reaching T_c<90 K for n7.     

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.     

Thermodynamic properties of two-dimensional charged spin-1/2 Fermi gases

Based on the mean-field theory, we investigate the thermodynamic properties of the two-dimensional (2D) charged spin-1/2 Fermi gas. Landé factor g is introduced to measure the strength of the paramagnetic effect. There is a competition between diamagnetism and paramagnetism in the system. The larger the Landé factor, the smaller the entropy and specific heat. Diamagnetism tends to increase the entropy, while paramagnetism leads to the decrease of the entropy. We find that there exists a critical value of Landé factor for the transition point due to the competition. The entropy of the system increases with the magnetic field when g < 0.58. With the growth of paramagnetism, when g > 0.58, the entropy first decreases with the magnetic field, then reaches a minimum value, and finally increases again. Both the entropy and specific heat increase with the temperature, and no phase transition occurs. The specific heat tends to a constant value at the hightemperature limit, and it approaches to zero at very low temperatures, which have been proved by the analytical calculation.     

Manipulating vortices in F=2 Bose-Einstein condensates through magnetic field and spin-orbit coupling

We investigate the vortex structures excited by Ioffe-Pritchard magnetic field and Dresselhaus-type spin-orbit coupling in F=2 ferromagnetic Bose-Einstein condensates. In the weakly interatomic interacting regime, an external magnetic field can generate a polar-core vortex in which the canonical particle current is zero. With the combined effect of spin-orbit coupling and magnetic field, the ground state experiences a transition from polar-core vortex to Mermin-Ho vortex, in which the canonical particle current is anticlockwise. For fixed spin-orbit coupling strengths, the evolution of phase winding, magnetization, and degree of phase separation with magnetic field are studied. Additionally, with further increasing spin-orbit coupling strength, the condensate exhibits symmetrical density domains separated by radial vortex arrays. Our work paves the way to explore exotic topological excitations in high-spin systems.