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     

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.     

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     

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.     

外加磁场压电悬臂梁能量采集系统的磁化电流法磁力研究

以外加磁场压电悬臂梁能量采集系统结构为研究对象, 根据磁化电流方法探讨了具有悬臂梁特征的系统结构的磁场作用力及其计算方法, 给出了相应的磁力计算模型, 并将计算结果与实验数据进行了对比. 研究表明, 磁化电流方法导出的磁力计算模型存在偏差, 其磁力计算误差随着磁铁间距缩小而增大. 通过引入悬臂梁末端磁铁的偏转角度, 对磁化电流法计算模型进行改进, 得到合理的外加磁场压电悬臂梁能量采集系统的磁力计算模型, 为该能量采集系统的进一步研究提供了可靠的磁力计算理论依据.     

Nonlocal pseudopotentials and magnetic fields

We show how to describe the coupling of electrons to nonuniform magnetic fields in the framework of the widely used norm-conserving pseudopotential approximation for electronic structure calculations. Our derivation applies to magnetic fields that are smooth on the scale of the core region. The method is validated by application to the calculation of the magnetic susceptibility of molecules within density functional theory (DFT) in the local density approximation. Our results are compared with high-quality all-electron DFT results obtained using Gaussian basis sets and another recently proposed pseudopotential formalism.     

Three-dimensional anisotropic harmonic oscillator in a magnetic field

The problem of the energy levels of a three-dimensional anisotropic harmonic oscillator in a uniform magnetic field with an arbitrary strength and orientation is exactly solved. It is shown that, in the magnetic field, the levels continue to be equidistant: the energy spectrum is a superposition of three groups of levels separated by the same spacing dependent on the field strength. The results obtained can be used in modeling the magneto-optical properties of diverse quantum-mechanical systems.     

On levitation of diamagnetic bodies in a magnetic field

Various methods for calculating the force characteristics of a suspension ensuring levitation of diamagnetic bodies of various origin and shape are considered. The method of calculation is based on the computation of the energy of interaction of a body upon its displacement from the center of suspension for an arbitrary configuration of the suspending field. The method of quasi-homogeneous approximation is considered and compared with the method for calculating the force characteristics based on the general formula for the magnetic energy. The necessary and sufficient conditions for conservative stability of the equilibrium state are formulated, and the stability domain is determined. It is shown that the stability domain depends on the size of the body. Calculations of force characteristics are performed specifically for the suspension of a diamagnetic sphere. The dependences of forces and stiffnesses on the magnetic field strength are obtained, which makes it possible to analyze the stability of confinement of the diamagnetic sphere in the field of the system of circular currents.     

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.     

Transport in magnetic graphene superlattice with Rashba spin-orbit interaction

Based on the transfer-matrix method, we have investigated the spin-dependent transport properties of magnetic graphene superlattice in the presence of Rashba spin-orbit interaction (RSOI). It is shown that the angular range of the spin transmission probability through magnetic graphene superlattice can be efficiently controlled by the number of barriers. As the number of magnetic barriers increases, the angular range of the transmission through the magnetic superlattice decreases, the gaps in the transmission and conductivity versus energy become wider. It is also found that the spin conductivities oscillate with the Fermi energy and RSOI strength. Specifically, when a magnetic field is present, the spin polarisation can be observed, whereas for the RSOI alone it is zero. Application of such a phenomenon to design a spin polarised electron device based on the graphene material is anticipated.     

The equatorial asymmetry of a magnetic field

Solution of the inverse problem for Parker’s one-dimensional mean-field dynamo model in a thin spherical layer is considered. The method allows the spatial distribution of energy sources, the α- and Ω-effects, to be found provided specified constraints occur on the solution. The highest ratio of the magnetic energies for the Northern and Southern hemispheres is discussed as such a constraint. The method is a modification of the Monte-Carlo technique; it is convenient for parallel computations and based on minimization of the cost function that characterizes the deviation of the model solution properties from the desired ones. The calculations show that the ratio of the energies in the hemispheres may exceed an order of magnitude for both poloidal and toroidal components of the magnetic energy. The ratio depends on the distance of the effective zone of the generation of the magnetic field from the equator and the number of harmonics in the spectrum. The greater this distance is and the higher the number of harmonics is, the stronger the magnetic field asymmetry can be.     

磁化等离子体环境对氢原子能级结构的影响

本文通过非微扰求解薛定谔方程, 研究了强磁场磁化的等离子体环境中的原子能级结构和辐射动力学过程. 在较宽的磁场强度范围和等离子体屏蔽参数范围内, 给出了氢原子基态以及低激发态的能级、辐射跃迁能量和振子强度等重要的原子参数, 定量地描述了强磁场和等离子体屏蔽共同作用的综合效应. 相关的结果有助于增进对极端环境下原子光谱结构的认识, 在等离子体光谱诊断和天文光谱观测方面有一定的借鉴意义. 关键词： 强磁场 CWDVR谱方法 能级结构 振子强度     

Estimation of the chiral magnetic effect considering the magnetic field response of the QGP medium

The magnetic field plays a major role in searching for the chiral magnetic effect in relativistic heavy-ion collisions. If the lifetime of the magnetic field is too short, as predicted by simulations of the field in vacuum, the chiral magnetic effect will be largely suppressed. However, the lifetime of the magnetic field will become longer when the QGP medium response is considered. We give an estimate of the effect, especially considering the magnetic field response of the QGP medium, and compare it with the experimental results for the background-subtracted correlator H at RHIC and LHC energies. The results show that our method explains the experimental results better at the top RHIC energy than at the LHC energy.     

Effect of magnetic field on beta processes in a relativistic moderately degenerate plasma

The effect of a magnetic field of arbitrary strength on the beta decay and crossing symmetric processes is analyzed. A covariant calculation technique is used to derive the expression for the squares of S-matrix elements of these reactions, which is also valid in reference frames in which the medium moves as a single whole along magnetic field lines. Simple analytic expressions obtained for the neutrino and antineutrino emissivities for a moderately degenerate plasma fully characterize the emissivity and absorbability of the studied medium. It is shown that the approximation used here is valid for core collapse supernovae and accretion disks around black holes; beta processes in these objects are predominantly neutrino reactions. The analytic expressions obtained for the emissivities can serve as a good approximation for describing the interaction of electron neutrinos and antineutrinos with the medium of the objects in question and hold for an arbitrary magnetic field strength. Due to their simplicity, these expressions can be included in the magnetohydrodynamic simulation of supernovae and accretion disks to calculate neutrino and antineutrino transport in them. The rates of beta processes and the energy and momentum emitted in them are calculated for an optically transparent matter. It is shown that the macroscopic momentum transferred in the medium increases linearly with the magnetic field strength and can substantially affect the dynamics of supernovae and accretion disks in the regions of a degenerate matter. It is also shown that the rates of beta processes and the energy emission for a magnetic field strength of B ? 10¹⁵ G typical of supernovae and accretion disks are lower than in the absence of field. This suppression is stronger for reactions with neutrinos.     

匀强磁场对水中气泡运动的影响

基于Rayleigh-Plesset方程, 考虑极性水分子在均匀磁场运动受到磁场力作用, 根据能量守恒建立了外磁场作用下单气泡运动的控制方程, 并对附加压强的大小、性质及对气泡运动的影响进行了计算和分析. 结果表明: 随磁场强度的增强, 附加压强线性增大, 气泡膨胀率降低, 最大半径减小, 气泡坍缩速度下降; 外加磁场引起的气泡振动变化规律与增大静态压具有相似的效果.     

Cu掺杂ZnO稀磁半导体磁电性能影响的模拟计算

在Cu重掺杂量摩尔数为0.02778–0.16667的范围内, 对ZnO掺杂体系磁电性能影响的第一性原理研究鲜见报道. 采用基于自旋密度泛函理论的平面波超软赝势方法, 用第一性原理计算了两种不同Cu单掺杂量Zn_1-xCu_xO (x=0.02778, 0.03125)超胞的能带结构分布和态密度分布. 结果表明, 掺杂体系是半金属化的稀磁半导体; Cu掺杂量越增加、相对自由空穴浓度越增加、空穴有效质量越减小、电子迁移率越减小、电子电导率越增加. 此结果利用电离能和Bohr半径进一步获得了证明, 计算结果与实验结果相符合. 在限定的掺杂量0.02778–0.0625 的条件下, Cu单掺杂量越增加、掺杂体系的体积越减小、总能量越升高、稳定性越下降、形成能越升高、掺杂越难. 在相同掺杂量、不同有序占位Cu双掺ZnO体系的条件下, 双掺杂Cu-Cu间距越增加, 掺杂体系磁矩先增加后减小; 当沿偏a轴或b轴方向Cu–O–Cu相近邻成键时, 掺杂体系会引起磁性猝灭; 当沿偏c轴方向Cu–O–Cu相近邻成键时, 掺杂体系居里温度能够达到室温以上的要求. 在限定的掺杂量0.0625–0.16667的条件下, 沿偏c轴方向Cu–O–Cu相近邻成键时, Cu 双掺杂量越增加, 掺杂体系总磁矩先增加后减小. 计算结果与实验结果变化趋势相符合.     

Advection of passive magnetic field by the Gaussian velocity field with finite correlations in time and spatial parity violation

Using the field theoretic renormalization group technique the model of passively advected weak magnetic field by an incompressible isotropic helical turbulent flow is investigated up to the second order of the perturbation theory (two-loop approximation) in the framework of an extended Kazantsev-Kraichnan model of kinematic magnetohydrodynamics. Statistical fluctuations of the velocity field are taken in the form of a Gaussian distribution with zero mean and defined noise with finite correlations in time. The two-loop analysis of all possible scaling regimes is done and the influence of helicity on the stability of scaling regimes is discussed and shown in the plane of exponents ? ? η, where ? characterizes the energy spectrum of the velocity field in the inertial range E ∞ k ^{1 ? 2ε}, and η is related to the correlation time at the wave number k which is scaled as k ^{?2 + η}. It is shown that in non-helical case the scaling regimes of the present vector model are completely identical and have also the same properties as those obtained in the corresponding model of passively advected scalar field. Besides, it is also shown that when the turbulent environment under consideration is helical then the properties of the scaling regimes in models of passively advected scalar and vector (magnetic) fields are essentially different. The results demonstrate the importance of the presence of a symmetry breaking in a given turbulent environment for investigation of the influence of an internal tensor structure of the advected field on the inertial range scaling properties of the model under consideration and will be used in the analysis of the influence of helicity on the anomalous scaling of correlation functions of passively advected magnetic field.     

固态氩弹性性质的量子力学从头计算

本文从量子力学第一性原理出发,用平面波赝势 (PWP)结合广义梯度近似(GGA)密度泛函理论方法,计算了零温下固态氩晶体0～82 GPa压力范围内的弹性性质,体系电子-离子相互作用采用硬赝势描述.计算结果与静高压实验数据良好相符,通过计算表明采取合理的方法和计算参数,惰性气体固态晶体高压下的力学性质可以比较准确地计算出来,这可为实验上难于进行研究的物质提供有意义的参考.     

Density of states in the magnetic ground state of the Friedel-Anderson impurity

By applying a magnetic field whose Zeeman energy exceeds the Kondo energy by an order of magnitude the ground state of the Friedel-Anderson impurity is a magnetic state. In recent years the author introduced the FAIR (Friedel Artificially Inserted Resonance) method to investigate the impurity properties. Within this FAIR approach the full excitation spectrum and the composition of the excitations is calculated and numerically evaluated. From the excitation spectrum the electron density of states is calculated. Majority and minority d-resonances are obtained. The width of the resonances is about twice as wide as the mean field theory predicts. This broadening reduces the height of the resonance curve and therefore the density of states by a factor of two. This yields an intuitive understanding for a previous result of the FAIR approach that it requires a much larger Coulomb interaction for the formation of a magnetic moment than the mean field theory.     

Exact energy principle in magnetic reconnection for current-sheet models

On the basis of an exact nonlinear energy principle, it is shown that the change in magnetic topology (i.e., reconnection) in a finite-domain system leads to the conversion of magnetic field energy to particle energy. However, it is also shown that the conversion efficiency gradually disappears as the system size increases. This principle is demonstrated with model current-sheet equilibria including Harris and Fadeev solutions, as well as a current-sheet equilibrium which contains a singular current layer. The finding that energy conversion in reconnection is highly dependent on the system size may have an important implication for numerical simulations performed under finite geometry.