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.     

基于伊辛模型的Fe0.5Mn0.1Al0.4 合金磁化强度和磁熵变蒙特卡洛模拟

基于伊辛模型的单自旋反转蒙特卡洛算法,考虑了粒子间的最近邻以及次近邻相互作用,研究了无序 合金的磁化强度和磁熵变。首先,强调了粒子间的次近邻相关作用对体系的磁性和热力学性质的影响,明确了次近邻相互作用系数,证实了低温合金阻挫的存在;其次,研究了在相变温度处(不同磁场下)磁化强度随外加磁场（温度）的变化情况以及磁性粒子对磁化强度的贡献,发现反铁磁性粒子Mn在低温区对 合金的相变起了主要作用,而高温区体系的相变是由铁磁性粒子Fe贡献的;最后,分析了体系在相变温度处磁熵变数值随外加磁场的变化情况以及磁熵变在不同的外磁场下随温度的变化情况,当外加磁场h=0.14时,Mn粒子在冻结温度处的平均磁化强度为零,体系处于最无序的状态,对应的磁熵变 达到了正向最大值,极值的位置对应于体系的相变温度。     

基于伊辛模型的Fe_(0.5)Mn_(0.1)Al_(0.4)合金磁化强度和磁熵变蒙特卡洛模拟

基于伊辛模型的单自旋反转蒙特卡洛算法,考虑了粒子间的最近邻以及次近邻相互作用,研究了无序Fe0.5Mn0.1Al0.4合金的磁化强度和磁熵变.首先,强调了粒子间的次近邻相关作用对体系的磁性和热力学性质的影响,明确了次近邻相互作用系数,证实了低温合金阻挫的存在;其次,研究了在相变温度处(不同磁场下)磁化强度随外加磁场(温度)的变化情况以及磁性粒子对磁化强度的贡献,发现反铁磁性粒子Mn在低温区对Fe0.5Mn0.1Al0.4合金的相变起了主要作用,而高温区体系的相变是由铁磁性粒子Fe贡献的;最后,分析了体系在相变温度处磁熵变数值随外加磁场的变化情况以及磁熵变在不同的外磁场下随温度的变化情况,当外加磁场H=0.14(a.u.)时,Mn粒子在冻结温度处的平均磁化强度为零,体系处于最无序的状态,对应的磁熵变ΔS(0.1,0.14)达到了正向最大值,极值的位置对应于体系的相变温度.     

Field dependent specific heat and longitudinal magnetization of the quantum magnet layer Cs2CuCl4: Anisotropy effects

We have addressed the specific heat and magnetization of an anisotropic spin-1/2 triangular Heisenberg antiferromagnet Cs₂CuCl₄ in the presence of magnetic field at finite temperature. We have investigated the behavior of thermodynamic properties by means of excitation spectrum in terms of a hard core bosonic representation. The effect of in-plane anisotropy on thermodynamic properties has also been studied via the bosonic model by Green’s function approach. This anisotropy is considered for exchange constants that couple spin components perpendicular to magnetic field direction. We have found the temperature dependence of the specific heat and longitudinal magnetization in the gapped field induced spin-polarized phase for various magnetic fields and anisotropy parameters. Furthermore we have studied the magnetic field dependence of specific heat and magnetization for various anisotropy parameters. Our results show temperature dependence of specific heat includes a peak so that its temperature position goes to higher temperature with increase of magnetic field. We have found the magnetic field dependence of specific heat shows a monotonic decreasing behavior for various magnetic fields due to increase of energy gap in the excitation spectrum.     

Bose-Einstein condensation of bouncing balls

Microscopic bouncing balls, i.e., particles confined within a positive one-half-dimensional gravitational potential, display Bose-Einstein condensation (BEC) not only in the thermodynamic limit but also in the case of a finite number of particles, and the critical temperature with a finite number of particles is higher than that in the thermodynamic limit. This system is different from the one-dimensional harmonic potential one, for which the standard result indicates that the BEC is not possible unless the number of particles is finite.     

三维简谐势阱中玻色-爱因斯坦凝聚的边界效应

在定义特征长度的基础上,应用Euler–MacLaurin公式,研究了理想玻色气体在三维简谐势阱中玻色-爱因斯坦凝聚的边界效应.结果表明:粒子的凝聚分数由于有限尺度和有限粒子数效应而减小,修正的凝聚分数和凝聚温度由于边界效应存在一个极大值,选择优化的最佳势阱参数,可以有效提高凝聚分数和凝聚温度;热容量的跃变存在边界效应和粒子数效应,选择合理的势阱参数时,热容量的跃变存在一个极小值.导出了简谐势阱中有限理想玻色气体的状态方程,揭示了压强的各向异性(或各向同性)取决于简谐势频率的各向异性(或各向同性).     

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.     

Extension of the BLOCH T(3/2) law to magnetic nanostructures: Bose-Einstein condensation

We report a newly observed phenomenon, namely, the observation of a visible anomaly in the Bloch T(3/2) law for the temperature dependence of magnetization of nanostructured ferromagnets, for which we give a thermodynamic explanation. Our interpretation extends the Bloch law by introducing the system's chemical potential and assumes a finite Bose-Einstein condensation temperature T(BE) of the magnons. Our extension involves accounting for the possibility of a magnon or magnetic entropy term, leading to a magnon chemical potential (hitherto omitted in the traditional derivation) which varies with temperature. The result is a subtle upturn of the magnetization curves of ferromagnetic nanoparticles in the 10 to 50 K temperature range. Here we show experimental data for nanomaterials and an outline of the extended theory which includes T(BE).     

Thermodynamics Properties of Confined Particles on Noncommutative Plane

We consider a system of $N$ particles living on the noncommutative plane in the presence of a confining potential and study its thermodynamics properties.Indeed, after calculating the partition function, we determine the corresponding internal energy and heat capacity where different corrections are obtained. In analogy with the magnetic field case, we define an effective magnetization and study its susceptibility in terms of the noncommutative parameter $\theta$. By introducing the chemical potential, we investigate the Bose-Einstein condensation for the present system. Different limiting cases related to the temperature and $\theta$ will be analyzed as well as some numerical illustration will be presented.     

Ferromagnetic resonance observation of a phase transition in magnetic field-aligned Fe2O3 nanoparticles

Fe₂O₃ hematite (alpha) nanoparticles suspended in the liquid phase of the liquid crystal 4,4-azoxyanlsole (PAA) are cooled below the freezing temperature (397 K) in a 4000 G dc magnetic field. The in field solidification locks the direction of maximum magnetization of the particles parallel to the direction of the applied dc magnetic field removing the effects of dynamical fluctuations of the nanoparticles on the magnetic properties allowing a study of the intrinsic magnetic properties of the nanoparticles as well as the anisotropic behavior of the ferromagnetic resonance (FMR) signal. Freezing in PAA allows temperature-dependent measurements to be made at much higher temperature than previous measurements. The field position, line width and intensity of the FMR signal as a function of temperature as well as the magnetization show anomalies in the vicinity of 200 K indicative of a magnetic transition, likely the previously observed Morin transition shifted to lower temperature due to the small particle size. Weak ferromagnetism is observed below T_c in contrast to the bulk material where it is antiferromagnetic below T_c. The Raman spectrum above and below 200 K shows no evidence of a change in lattice symmetry associated with the magnetic transition.     

Thermodynamic quantities in a Bose-Einstein gas at the quantum limit in a strong magnetic field close to the critical temperature

We have determined the thermodynamic functions (the translational kinetic energy, the pressure, the chemical potential, and the specific heat jump) in a degenerate Boson gas, close to the temperature where a Bose-Einstein condensation takes place into the first Landau energy level in a strong magnetic field. It is shown that the rearrangement of the energy spectrum and the number density of the quantum states for charged particles in a quantizing magnetic field cause the thermodynamic functions for a degenerate Boson system to differ qualitatively and quantitatively from the analogous quantities in the absence of a field.Government Institute, Brest. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 51–55, January, 1993.     

Extended Hubbard model in the presence of a magnetic field

Within the Green’s function and equations of motion formalism it is possible to exactly solve a large class of models useful for the study of strongly correlated systems. Here, we present the exact solution of the one-dimensional extended Hubbard model with on-site U and first nearest neighbor repulsive V interactions in the presence of an external magnetic field h, in the narrow band limit. At zero temperature our results establish the existence of four phases in the three-dimensional space (U, n, h) – n is the filling – with relative phase transitions, as well as different types of charge ordering. The magnetic field may dramatically affect the behavior of thermodynamic quantities, inducing, for instance, magnetization plateaus in the magnetization curves, and a change from a single to a double-peak tructure in the specific heat. According to the value of the particle density, we find one or two critical fields, marking the beginning of full or partial polarization. A detailed study of several thermodynamic quantities is also presented at finite temperature.     

New micromagnetic states of magnetically soft nanoparticles with a nearly cubic shape

The ground state of nonellipsoidal particles can be inhomogeneous due to the effect of a demagnetizing field. The approach proposed here for studying such particles is based on the combination of symmetry analysis and perturbation theory. The general formulation of this approach, which makes it possible to analyze weakly inhomogeneous states for particles with a complex shape, is considered. The ground state of cubic particles of magnetically soft materials is calculated analytically, and the effect of small strains of cubic particles on the magnetization distribution in the particles is investigated. It is shown for the example of magnetically soft cubic particles that even a small deviation of the particle shape from symmetrical may result in the realization of a special magnetic state in such particles, in which the symmetry in the magnetization distribution is lower than the particle symmetry. A change in the parameters of a particle can substantially modify its magnetic properties and may even induce a phase transition to a state with a different symmetry.     

Probing anomalous longitudinal fluctuations of the interacting Bose gas via Bose-Einstein condensation of magnons

The emergence of a finite staggered magnetization in quantum Heisenberg antiferromagnets subject to a uniform magnetic field can be viewed as Bose-Einstein condensation of magnons. Using nonperturbative results for the infrared behavior of the interacting Bose gas, we present exact results for the staggered spin-spin correlation functions of quantum antiferromagnets in a magnetic field at zero temperature. In particular, we show that in dimensions 1相似文献   

The magnetized d-dimensional ideal paragas

The magnetic properties of a d-dimensional uncharged ideal paragas in a uniform magnetic field are examined. For parastatistics parameter p = ∞ (bosons) there is Bose-Einstein condensation for d/ > 1 with spontaneous magnetization, and for 1<d/2 there is a divergent magnetic susceptibility at zero magnetic field. For finite p (parafermions) we obtained the asymptotic limit behavior of low and high temperature of the magnetic susceptibility. The crossover between these limits is evaluated numerically, observing that the parafermions can be characterized by Fermi-Dirac behavior.     

Phase transitions for an ideal Bose condensate trapped in?a?quartic potential

Based on the classification scheme of phase transitions, we study the phase transitions for an ideal Bose gas with a finite number of particles confined in a three-dimensional quartic trap. We show that the phase transition of an ideal Bose gas in the three-dimensional quartic trap is of third order for finite particle numbers, quite different from the fact that the phase transition is of first order in the thermodynamic limit. We discuss the effects of finite particle numbers on the nature of the phase transitions, and determine the dependence of transition temperature on particle number.     

Magnetic properties and the mechanism of formation of the uncompensated magnetic moment of antiferromagnetic ferrihydrite nanoparticles of a bacterial origin

The magnetic properties of the superparamagnetic ferrihydrite nanoparticles that form as a result of the vital activity of Klebsiella oxytoca bacteria are studied. Both an initial powder with an average number of iron atoms N _Fe ～ 2000–2500 in a particle and this powder after annealing at 140°C for 3 h in air are investigated. The following substantial modifications of the magnetic properties of the ferrihydrite nanoparticles are detected after annealing: the superparamagnetic blocking temperature increases from 23 to 49.5 K, and the average magnetic moment of a particle increases (as follows from the results of processing of magnetization curves). The particles have antiferromagnetic ordering, and the magnetic moment resulting in the superparamagnetism of the system appears due to random spin decompensation inside the particle. For this mechanism, the number of uncompensated spins is proportional to the number of magnetically active atoms raised to the one-half power, and this relation holds true for the samples under study at a good accuracy. The possible causes of the detected shift of magnetic hysteresis loops at low temperatures upon field cooling are discussed.     

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.     

Thermodynamics of a Bose-Einstein condensate with free magnetization

We study thermodynamic properties of a gas of spin 3(52)Cr atoms across Bose-Einstein condensation. Magnetization is free, due to dipole-dipole interactions. We show that the critical temperature for condensation is lowered at extremely low magnetic fields, when the spin degree of freedom is thermally activated. The depolarized gas condenses in only one spin component, unless the magnetic field is set below a critical value, below which a nonferromagnetic phase is favored. Finally, we present a spin thermometry efficient even below the degeneracy temperature.     

Boundary and particle number effects on the thermodynamic properties of trapped ideal Bose gases

The ideal noninteracting Bose gases trapped in a generic power-law potential in an any-dimensional space are studied. We present theoretical results of the corrections of thermodynamic properties due to finite particle number effects. The calculation uses the Euler-Maclaurin approximation to simplify the condensate fraction, and it also uses the Maslov index to discuss the boundary effect. Recently BEC (Bose-Einstein Condensation) has also been observed in a microelectronic chip; therefore, with a similar microstructure, we can obtain the effects of a rigid wall in a trap that have never been found before.Received: 3 January 2003, Published online: 23 July 2003PACS: 05.30.-d Quantum statistical mechanics