Quantum entanglement in a finite temperature interacting electron gas

The entanglement between two electrons in a degenerate electron gas is studied as a function of their separation and of temperature. It is found that interaction leads to a suppression of the entanglement distance.     

Entropy squeezing of the field interacting with a nearly degenerate V-type three-level atom

The position- and momentum-entopic squeezing properties of the optical field in the system of a nearly degenerate three-level atom interacting with a single-mode field are investigated. Calculation results indicate that when the field is initially in the vacuum state, it may lead to squeezing of the position entropy or the momentum entropy of the field if the atom is prepared properly. The effects of initial atomic state and the splitting of the excited levels of the atom on field entropies are discussed in this case. When the initial field is in a coherent state, we find that position-entropy squeezing of the field is present even if the atom is prepared in the ground state. By comparing the variance squeezing and entropy squeezing of the field we confirm that entropy is more sensitive than variance in measuring quantum fluctuations.     

On the energy losses of slow ions in an interacting degenerate electron gas

Energy losses of slow ions with velocitiesv?v _F (v _F is the Fermi velocity) in an interacting degenerate electron gas are calculated on the basis of the dielectric theory of Singwi. It is shown that the local field effects taken into account in this theory lead to an increase of the energy losses as compared with the Lindhard stopping power by a factor which can reach a few tens of percent for some compressed ICF plasmas. Corresponding factors for simple metals are as much as 2–3 and are in agreement with experiment.     

The specific heat of a degenerate electron gas

The internal energy of a degenerate electron gas is evaluated for finite temperature to first order ine ² by applying the Sommerfeld method to the grand partition function. The specific heat is obtained correctly by temperature differentiation in which the shift of the Fermi momentum from the ideal gas value is taken into consideration. Thus, this theory differs from those given previously by Pines, Gell-Mann and others. In fact, there appears no divergence such as encountered by Gell-Mann in his approximate approach. The specific heat thus evaluated increases slightly withr _s in agreement with recent experimental data on alkali metals. This work was supported by the National Science Foundation.     

Single-particle spectrum of the degenerate electron gas

Extensive numerical results in the Random Phase Approximation are presented for the spectral weight function, the momentum distribution, and the density of states of the degenerate electron gas over a range of metallic densities. The single-particle spectrum contains not only the damped quasiparticle but also structure due to plasmon effects. At low momenta there is a second elementary excitation of appreciable weight. The density of states has a satellite band at energies more than the plasma energy below the Fermi level. The results confirm the main features of an earlier analysis using a simplified dielectric function.     

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.     

Thermodynamic functions of degenerate magnetized electron gas

The Fermi energy, pressure, internal energy, entropy, and heat capacity of completely degenerate relativistic electron gas are calculated by numerical methods. It is shown that the maximum admissible magnetic field on the order of 10⁹ G in white dwarfs increases the pressure by a factor of 1.06 in the central region, where the electron concentration is ∼10³³ cm⁻³, while the equilibrium radius increases by approximately a factor of 1.03, which obviously cannot be observed experimentally. A magnetic field of ∼10⁸ G or lower has no effect on the pressure and other thermodynamic functions. It is also shown that the contribution of degenerate electron gas to the total pressure in neutron stars is negligible compared to that of neutron gas even in magnetic fields with a maximum induction ∼10¹⁷ G possible in neutron stars. The neutron beta-decay forbiddeness conditions in a superstrong magnetic field are formulated. It is assumed that small neutron stars have such magnetic fields and that pulsars with small periods are the most probable objects that can have super-strong magnetic fields.     

Single-particle spectrum of the degenerate electron gas

The single-particle spectrum of an interacting electron gas is discussed. There is a characteristic structure in the spectral weight function at energies that differ from the quasi-particle energy by energies of the order of the plasma energy. This structure is due to the singular Coulomb potential and the plasmon part of the effective interaction at long wavelengths. For momenta deep inside the Fermi sea a new elementary excitation of appreciable strength appears. It can be interpreted as a coupled mode of holes and plasmons.     

Form of the memory function for a degenerate electron gas with elastic scatterers

The high frequency response of an electron gas with elastic scatterers can be described by a Drude equation with a memory term, which is an integral over a kernel times the square of the scattering potential. In the momentum (and frequency or time) representation, this kernel is discontinuous at the diameter of the Fermi sphere.In the time representation it has the causality property. As a function of space it shows Friedel oscillations.     

Magnetic response of a two-dimensional degenerate electron gas in nanostructures with cylindrical symmetry

An investigation is made of the magnetic response of nanostructures with cylindrical symmetry located in a longitudinal magnetic field. Analytic expressions are obtained for the magnetic moment of the nanostructures, cylinders and bracelets. It is shown that the magnetic moment describes Aharonov-Bohm oscillations. The profile of the oscillations and the position of the oscillation maxima are studied. In the limit T→0 the curves of the magnetic response as a function of the magnetic field flux contain “beak”-shaped kinks, and the positions of the points at which these kinks occur are determined. The temperature dependence of the magnetic response is studied and the influence of the spin-magnetic interaction on the magnetic response of the nanostructures is examined. It is shown that this interaction destroys the periodicity of the magnetic response with respect to flux and gives rise to a monotonic term in the response. Zh. éksp. Teor. Fiz. 115, 1450–1462 (April 1999)     

Kinetic equation for a weakly interacting classical electron gas

A kinetic equation is derived for the two-time phase space correlation function in a dilute classical electron gas in equilibrium. The derivation is based on a density expansion of the correlation function and the resummation of the most divergent terms in each order in the density. It is formally analogous to the ring summation used in the kinetic theory of neutral fluids. The kinetic equation obtained is consistent to first order in the plasma parameter and is the generalization of the linearized Balescu-Guersey-Lenard operator to describe spatially inhomogeneous equilibrium fluctuations. The importance of consistently treating static correlations when deriving a kinetic equation for an electron gas is stressed. A systematic derivation as described here is needed for a further generalization to a kinetic equation that includes mode-coupling effects. This will be presented in a future paper.     

Magnetism of a relativistic degenerate electron gas in a strong magnetic field

The magnetization and magnetic susceptibility of a degenerate electron gas in a strong magnetic field in which electrons are located on the ground Landau level and the electron gas has the properties of a nonlinear paramagnet have been calculated. The paradoxical properties of the electron gas under these conditions??a decrease in the magnetization with the field and an increase in the magnetization with the temperature??have been revealed. It has been shown that matter under the corresponding conditions of neutron stars is a paramagnet with a magnetic susceptibility of ?? ?? 0.001.