The magnetized electron gas in terms of Hurwitz zeta functions

We obtain explicit expressions for thermodynamic quantities of a relativistic degenerate free electron gas in a magnetic field in terms of Hurwitz zeta functions. The formulation allows for systematic expansion in all regimes. Three energy scales appear naturally in the degenerate relativistic gas: the Fermi energy E_F, the temperature T and an energy related to the magnetic field or Landau level spacing, eB/E_F. We study the cold and warm scenarios, T⪡eB/E_F and eB/E_F⪡T, respectively. We reproduce the oscillations of the magnetization as a function of the field in the cold regime and the dilution of them in the warm regime.     

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.     

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.     

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.     

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.     

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 potential of a degenerate gas of quasirelativistic electrons

We consider a degenerate gas of quasirelativistic electrons in a state of equilibrium. Based on the functional integral method in the RPA we obtain the thermodynamic potential of the system. We take into account the contributions of the spin-spin, spin-orbit, and contact interactions. We calculate the average energy for one particle at the absolute zero of temperature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 70–75, September, 1986.     

Electron polarization in nonrelativistic nondegenerate magnetized electron gas

For a nondegenerate nonrelativistic electron system, taking account of the minimum of its total energy, the population of the Landau electron levels by electrons with intrinsic magnetic moments parallel and antiparallel to the external magnetic field is determined, as a function of the external magnetic field strength H. The results are then compared with analogous data obtained by other authors without taking the minimum of the system’s total energy into account. Brestsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 14–19, February, 1997.     

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.     

Thermodynamic functions of electron gas on the semiconductor nanotube surface in a magnetic field

Thermodynamic functions have been calculated in the effective mass approximation for degenerate and nondegenerate electron gases on the semiconductor cylindrical nanotube surface in a longitudinal magnetic field. The Laplace transform linking the density of states and the statistical sum has been used. The thermodynamic quantities of degenerate electron gas undergo the de Haas-van Alphen oscillations with the electron Fermi energy change and the Aharonov-Bohm oscillations with the magnetic flux change within the semiconductor tube cross section. The quantities related to nondegenerate gas oscillate only with the change of magnetic flux. A peak has been found in the nondegenerate gas heat capacity-temperature diagram. A limiting process to 2D electron gas on plane has been carried out.     

Superconductivity of the magnetized electron gas of a quantum cylinder

A microscopic theory of superconductivity is developed for the magnetized electron gas on a cylindrical surface. The Gibbs free energy is calculated for the superconducting system. A gap equation is derived that determines the critical temperature as a function of the quantum-cylinder dimensions and the Aharonov-Bohm parameter. It is shown that the gap not only exhibits Aharonov—Bohm oscillations, but also oscillates with varying curvature of the cylindrical surface.     

Resonant mechanism of axion photoproduction in a magnetized electron gas

It was shown that the contribution of diagrams with electron-positron vacuum excitation in a strong magnetic field B ? B ₀ = m ²/e = 4.41 × 10¹³ G in the Compton mechanism of axion production γe → ae at temperatures on the order of the axion mass exceeds the contribution of the “simple” Compton diagram and the contribution of the neutrino production γe → (ν\(\bar \nu \))e to the radiation power by many orders of magnitude. The conclusion is made on the probable axionic nature of the cold hidden mass of the Universe.     

Dielectric properties of a magnetized electron gas in a nanotube

A quantum expression is derived for the longitudinal permittivity of a magnetized electron gas in a quantum cylinder. The asymptotics of the dispersion law are calculated for longitudinal plasma waves in a degenerate electron gas. The approximations of the weak and strong spatial dispersions are considered. It is shown that the longitudinal permittivity is an oscillating function of the magnetic flux through the cross section of the nanotube.     

Effects of confinement on a magnetized ideal gas: I. The electron gas

Using the framework of the grand canonical ensemble the effects of a two (or three) dimensional confinement (harmonic) potential on the magnetic properties of an ideal electron gas are investigated. The high temperature results for the magnetic moment obtained by Felderhof and Raval are generalized to take into account the spin. At low temperature the confinement potential introduces a new oscillatory phenomena besides a modification or even a destruction of the de Haas-van Alphen effect. The changes in Landau diamagnetism are also analysed.     

Magnetic moment of a two-dimensional degenerate electron gas in mesoscopic samples

The orbital magnetism of two-dimensional electrons in mesoscopic samples is studied in models where the interaction between electrons is neglected. Various geometries are considered as there are disc, plaquette, bracelet with hard wall confinement and also a confinement with a parabolic potential. We calculate the average magnetic moment which means an average with respect to size fluctuations and de Haas-van Alphen oscillations which arise in the case of a sharp Fermi cutoff. We see three distinct ranges in the magnetic field: (i) small field region where perturbation theory applies; (ii) moderate fields where edge currents play a prominent role; and (iii) the high field range with a Landau type susceptibility. In a quasiclassical picture, the electronic orbits are not qualitatively changed by a magnetic field in (i); skipping orbits are important in (ii); and in (iii), the cyclotron radius is smaller than the sample size. As a rule, we find an enhancement of the magnetic response which increases with k_FL, that is, with sample size divided by the Fermi wave length. Also, we have found out that the quasiclassical approximation fails in the calculation of the magnetic properties; on the other hand, we have seen no essential differences between the canonical ensemble (fixed particle number) and the grand canonical ensemble (chemical potential given). In the case of plaquettes, in particular for samples in the form of squares, we have found agreement with experimental results by Lévy, Reich, Pfeiffer and West.     

Thermodynamic properties of electron gas in complex-shaped quantum well

Thermodynamic properties of degenerate two-dimensional electron gas in complex-shaped quantum well are studied. We determine the equation of state, chemical potential, entropy and heat capacity of the electron gas. An influence of profile and parameters of the quantum well on thermodynamic characteristics are investigated.