Hydrogen recombination in the early Universe in the presence of a magnetic field

Hydrogen recombination in the earlyUniverse in the presence of amagnetic field is studied. An equation for the recombination temperature in the presence of a magnetic field is obtained. The limiting cases of weak and strong magnetic fields are examined. A critical field above which the system being considered is in the atomic-hydrogen phase at any temperature is shown to exist. The relative shift of the recombination temperature in a magnetic field is estimated, and it is shown that this shift is small.     

Self-consistent transport equations for the electron-impurity system in a magnetic field

General transport equations for a system of independent electrons in a random array of impurities of arbitrary range and in a magnetic field of arbitrary strength are derived on the basis of conventional perturbation theory, and the general structure of the transverse transport coefficients is discussed. Contrary to kinetic theory, within this framework it is easy to formulate “conserving” approximations, which include collision-broadening effects self-consistently. It is demonstrated, how for high magnetic field explicit results for the transverse transport coefficients can be obtained, which are free of the divergencies appearing in the kinetic theory.

     

On Suhl's dispersion equations for dilute magnetic alloys in a finite magnetic field

The system of six coupled, nonlinear, singular integral equations, devised by Suhl to treat the problem of a spin 1/2 magnetic impurity in a finite magnetic field is shown to be reducible to a single integral equation. Analytic properties and symmetries of the system are discussed, which may serve as a guideline for numerical studies of the final integral equation. The first few steps of an iteration in terms of the magnetic field strength are carried out analytically.On leave from the Institut für Theoretische Physik der Universität Köln.     

On Suhl's dispersion equations for dilute magnetic alloys in a finite magnetic field

A one dimensional, nonlinear, singular integral equation was recently shown to be equivalent to Suhl's dispersion equations for the Kondo-problem of a half-spin magnetic impurity in a finite magnetic field. We investigate this integral equation further analytically and numerically and obtain numerical solutions which we use for a calculation of transport coefficients. The normal part of the scattering potential of the magnetic impurity is included via ans-wave phase shift. The transport coefficients are universal functions of the ratiosT/T _K andB/B _K of the temperatureT and the zero magnetic field Kondo-temperatureT _K and of the magnetic inductionB and the Kondo magnetic inductionB _K. We find maxima in the electrical and thermal resistivities as functions ofT/T _K forBB _K. These are typical Kondo phenomena, and can be influenced by. Interference of and the phases of Kondo-scattering amplitudes leads to dramatic effects in the thermopower and the Hall coefficient.SFB 125The numerical part of this work was performed at the Institut für Festkörperforschung, Kernforschungsanlage Jülich, F.R. Germany     

Lagrangian equations of motion for a massive conductor in a magnetic field

The motion of a nonferromagnetic massive conductor is considered in a quasi-inhomogeneous, varying magnetic field. It is shown that the equations of motion can be written in Lagrangian form.SUNTs. M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 63–69, July, 1994.     

An Asymptotic Preserving scheme for the Euler equations in a strong magnetic field

This paper is concerned with the numerical approximation of the isothermal Euler equations for charged particles subject to the Lorentz force (the ‘Euler–Lorentz’ system). When the magnetic field is large, or equivalently, when the parameter ε$\epsilon$ representing the non-dimensional ion cyclotron frequency tends to zero, the so-called drift-fluid (or gyro-fluid) approximation is obtained. In this limit, the parallel motion relative to the magnetic field direction splits from perpendicular motion and is given implicitly by the constraint of zero total force along the magnetic field lines. In this paper, we provide a well-posed elliptic equation for the parallel velocity which in turn allows us to construct an Asymptotic-Preserving (AP) scheme for the Euler–Lorentz system. This scheme gives rise to both a consistent approximation of the Euler–Lorentz model when ε$\epsilon$ is finite and a consistent approximation of the drift limit when ε→0$\epsilon \to 0$. Above all, it does not require any constraint on the space and time-steps related to the small value of ε$\epsilon$. Numerical results are presented, which confirm the AP character of the scheme and its Asymptotic Stability.     

Baryogenesis in the early Universe

We review various attempts to create the observed baryon asymmetry of the Universe. In particular, we consider models of GUT baryogenesis, baryogenesis via leptogenesis, the Affleck-Dine mechanism, electroweak baryogenesis and baryogenesis via topological defects and primordial black holes.     

Spontaneous magnetization of the vacuum and the strength of the magnetic field in the hot Universe

Intergalactic magnetic fields are assumed to have been spontaneously generated at the reheating stage of the early Universe, due to vacuum polarization of non-Abelian gauge fields at high temperature. The fact that the screening mass of this type of fields has zero value was discovered recently. A procedure to estimate their field strengths, B(T), at different temperatures is here developed, and the value B(T _ew)∼10¹⁴ G at the electroweak phase transition temperature is derived by taking into consideration the present value of the intergalactic magnetic field strength, B ₀∼10⁻¹⁵ G, coherent on the ∼1 Mpc scale. As a particular case, the standard model is considered and the field scale at high temperature is estimated in this case. Model-dependent properties of the phenomena under investigation are briefly discussed, too.     

On a remarkable electromagnetic field in the Einstein Universe

We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the 3-sphere \(S^3\). The conformal equivalence between Minkowski’s spacetime and (a region of) the Einstein cylinder is then exploited in order to obtain a knotted, finite energy, radiating solution of the Maxwell equations in flat spacetime. We also discuss similar electromagnetic fields in expanding closed Friedmann models, and compute the matter content of such configurations.     

Inflation of the early cold Universe filled with a nonlinear scalar field and a nonideal relativistic Fermi gas

We consider a possible scenario for the evolution of the early cold Universe born from a fairly large quantum fluctuation in a vacuum with a size a ₀ ? l _P (where l _P is the Planck length) and filled with both a nonlinear scalar field φ, whose potential energy density U(φ) determines the vacuum energy density λ, and a nonideal Fermi gas with short-range repulsion between particles, whose equation of state is characterized by the ratio of pressure P(n _F ) to energy density ε(n _F ) dependent on the number density of fermions n _F . As the early Universe expands, the dimensionless quantity ν(n _F ) = P(n _F )/ε(n _F ) decreases with decreasing n _F from its maximum value ν_max = 1 for n _F → ∞ to zero for n _F → 0. The interaction of the scalar and gravitational fields, which is characterized by a dimensionless constant ξ, is proportional to the scalar curvature of four-dimensional space R = κ[3P(n _F )–ε(n _F )–4λ] (where κ is Einstein’s gravitational constant), and contains terms both quadratic and linear in φ. As a result, the expanding early Universe reaches the point of first-order phase transition in a finite time interval at critical values of the scalar curvature R = R _c =–μ²/ξ and radius a _c ? a ₀. Thereafter, the early closed Universe “rolls down” from the flat inflection point of the potential U(φ) to the zero potential minimum in a finite time. The release of the total potential energy of the scalar field in the entire volume of the expanding Universe as it “rolls down” must be accompanied by the production of a large number of massive particles and antiparticles of various kinds, whose annihilation plays the role of the Big Bang. We also discuss the fundamental nature of Newton’ gravitational constant G _N .