Thermodynamic functions of a nonrelativistic degenerate neutron gas in a magnetic field

The Fermi energy, partial concentrations of polarized neutrons, pressure, and volume energy density of a degenerate nonrelativistic neutron gas in a magnetic field are calculated using numerical methods taking into account the anomalous magnetic moment of a neutron. The results of calculations are a generalization of relations underlying the Oppenheimer-Volkov model of a neutron star to the case of an applied magnetic field. An ultrastrong (up to 10¹⁷ G) magnetic field changes the pressure and internal energy of the star and affects it static configuration and evolution. It is shown that a degenerate neutron gas in ultrastrong and weak magnetic fields is paramagnetic; the corresponding values of magnetic susceptibility differ by a factor on the order of unity. The possibility of experimentally verifying the results from analysis of pulsar-emitted radiation is discussed.     

Temperature corrections to the thermodynamic functions of a degenerate neutron gas in a magnetic field

Temperature corrections to the basic thermodynamic functions calculated in our earlier publication [1] for a degenerate neutron gas in a magnetic field are determined taking into account the anomalous magnetic moment of a neutron. The heat capacity and entropy of the degenerate neutron gas, as well as the temperature correction to the magnetic susceptibility, are also calculated. Additional arguments supporting the effect of an increase in the pulse frequency of pulsars mentioned in the previous publication are formulated; the results of that publication are refined.     

Response functions of a degenerate electron gas: The memory-function kinetic equation approach

The quantum kinetic memory function is discussed in relation to the different kω dependences of density and spin responses and to plasmon damping. A memory function, derived from the Hartree plus screened exchange approximation, reproduces the required kω dependence.     

Stationary Boltzmann equation for a degenerate gas in a slab: Boundary value problem and hydrodynamics

The boundary value problem for the stationary Boltzmann equation for a model gas in a plane slab is solved in full generality. The asymptotic behavior as the size of the slab goes to infinity is studied via a Chapman-Enskog expansion.     

Geometry of equilibrium configurations in the Ising model

We derive microscopically precise identities for the geometry of small clusters in the equilibrium states of the two-dimensional Ising model with emphasis on near-critical phenomena.     

中子星中简并电子气体的临界磁化

中子星内部的电子处于高度简并或完全简并的状态,电子磁矩(包括内禀磁矩和朗道反磁矩)的取向不是随机的,而是呈现出极强的磁化行为.考虑了磁化后的磁诱导方程要改写,改写后的方程添加了新的磁场生成项,更重要的改变是等效磁扩散系数变小了(顺磁情况),在临界情况(等效扩散系数等于零),磁场在磁生成项的作用下增加直到抑制机理出现,朗道反磁矩就是在这个时候变得越来越重要.磁场增加的最终结果使中子星局域磁场成为振荡的,对外看来有可能成为磁星. 关键词： 中子星 简并 磁化     

相对论简并电子气体的磁化

中子星内部的致密电子是高度简并的相对论气体, 其输运性质与中子星磁或热的观测现象密切相关, 被认为是中子星磁场的主要载体. 外磁场中电子的朗道能级是分立的且高度简并的, 与无外场时的能量差决定 了系统的磁化程度, 用量子统计的方法可计算理想相对论电子气体的磁化率. 结果表明弱场条件下的磁化率在数量级上接近白矮星的10^-3. 强磁场下的磁化呈现出类似在某些低温金属中出现的de Haas-van Alphen 震荡效应, 高次谐频的震荡幅度有可能超出临界磁化时的磁化率. 表明中子星内部有可能存在非稳定的磁化过程, 发生类似气液转化的一级相变过程, 出现两种磁化共存的稳定态或过冷磁化的亚稳态(若不同磁化态间存在表面能). 从亚稳态向稳定态的突然转化可能与磁星的辐射有关, 可以解释在磁星巨闪过程中观测到的额外辐射问题.     

Single-site approximations for equilibrium and transport properties of random alloys

Introducing the configuration averaging as a projection operator, we propose a new formulation of the average t-matrix and the coherent potential approximations that treats on equal footing both the equilibrium and the residual transport properties of disordered alloys.     

Relative equilibrium and collapse configurations of heterogeneous vortex triple rings

Configurations of point vortices in a 2D fluid that are placed at the vertices of concentric regular m-gons, i.e. point vortex rings, are considered. The number of configurations that rotate uniformly-relative equilibria-is shown to be finite in the case of three rings with arbitrary circulations, subject to a few circulation constraints. Similar finiteness results for collapse configurations of three rings are also obtained, and an effective computational method is described.     

Motion of a particle in the field of a rotating body in the post-Newtonian approximation. Alternative solutions

The components of the gravitational field are compared in the post-Newtonian approximation in the geometric (Einstein tensor) and field (Maxwellian vector form) theories of gravitation. The fundamental difference of these fields in the motion of a test particle is shown. The feasibility of qualitative detection of the vortex component of the gravitational field is found experimentally. The scheme for an alternate experiment is given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 15–18, May, 1990.The author thanks A. S. Lantsev for the experimental part of the article presented here.     

Stability of symmetries for equilibrium configurations ofN particles in three dimensions

We consider equilibrium configurations ofn identical particles in three dimensions interacting via two-body potentials depending only on the distance. The symmetry group of a given configuration is defined as the subgroup of isometries which leaves it invariant, up to permutations of the particles. We prove the stability of the symmetry in the following sense: the symmetry group of an equilibrium configuration is the same for the neighboring equilibria arising from any small enough perturbation of the initial potential. Furthermore, for a large class of realistic potentials, the existence of nontrivial symmetries is proved, thus giving a completely geometrical, although partial, approach to the classical crystal problem.     

Classification of states and determination of wave functions in the case of almost - degenerate configurations

Appropriate unitary groups and their expansions are proposed for classifying states in overlapping configurations of atomic spectra. Overlapping configurations are considered as a single combined configuration. The coefficients of the wave functions of pure configurations are then obtained using only group methods from the properties of the group generators, and do not depend on the energy matrix.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 21–23, March, 1984.     

Observation of dipole-dipole interaction in a degenerate quantum gas

We have investigated the expansion of a Bose-Einstein condensate of strongly magnetic chromium atoms. The long-range and anisotropic magnetic dipole-dipole interaction leads to an anisotropic deformation of the expanding chromium condensate which depends on the orientation of the atomic dipole moments. Our measurements are consistent with the theory of dipolar quantum gases and show that a chromium condensate is an excellent model system to study dipolar interactions in such gases.     

Neutron radii in nuclei and the neutron equation of state

The root-mean-square radius for neutrons in nuclei is investigated in the Skyrme Hartree-Fock model. The main source of theoretical variation comes from the exchange part of the density-dependent interaction which can be related to a basic property of the neutron equation of state. A precise measurement of the neutron radius in 208Pb would place an important new constraint on the equation of state for neutron matter. The Friedman-Pandharipande neutron equation of state would lead to a very precise value of 0.16+/-0.02 fm for the difference between the neutron and the proton root-mean-square radius in 208Pb.     

Stability and accuracy of spatial approximations for wave equation tidal models

Amplitude and phase characteristics for numerical approximations to the shallow water wave equation are obtained for linear and quadratic finite elements, for finite difference approximations, for non-constant bathemetry, and for uneven node spacing. Stability is shown to require non-zero friction as well as satisfaction of a Courant constraint. Lumping is shown to reduce the Courant constraint for stability while higher order and quadratic finite element approximations require a more restrictive constraint than their second order and linear finite element counterparts. The amplitude of the propagation factor for stable schemes and propagating waves is seen to be independent of the Courant number and type of numerical approximation. Although the higher order and quadratic schemes provide better propagation of the low and moderate frequency waves, the highest frequency waves (2Δx) are better propagated by low order numerical methods.     

Test of the Wu-Feenberg and F2 approximations in neutron matter and liquid 3He

It is shown that the Wu-Feenberg (WF) approximation for the radial distribution of a Slater-Jastrow function can be reformulated in a way which should improve the approximation in low orders, as judged by the test case where the Jastrow factor is replaced by the boson ground state of the Hamiltonian of interest. It is also shown that the lowest order of another approximation scheme due to Paulick and Campbell appears to be a partial resummation of the WF approximation. The energy expectation value is evaluated for “homework” neutron matter and liquid ³He using these approximations and compared to the Monte Carlo evaluation of the same quantity by Ceperley, Chester and Kalos (CCK) and the FHNC/4 approximation. There is excellent agreement for neutron matter in the density range 0.17 to 4.0 fm^?3; the agreement for liquid ³He is fair but has room for improvement.