Suppression of degeneracy of Fermi gases of charged particles in a strong magnetic field

The suppression of degeneracy of ultrarelativistic electron and nonrelativistic proton gases is considered as a function of temperature and magnetic field strength. It is shown that at absolute zero the degeneracy of nonrelativistic proton and relativistic electron gases of equal concentrations is suppressed at the same values of magnetic field strength exceeding considerably the values at which these particles fill the lower Landau level completely.Education Institute, Brest. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 85–90, June, 1992.     

Verallgemeinerung der Methode der singulären Normallösungen für isotherme irreversible Vlasov-Systeme

Irreversible Vlasov systems, i.e. systems governed by a Vlasov-type kinetic equation including entropy-producing collision terms, are treated by the techniques of singular normal modes and singular integral equations using a new indirect method which renders possible a straightforward generalization of the Case formalism as developed originally for collision-free Vlasov plasmas. This method is in contrast to a more complex method given by the present authors for the first application of the singular normal mode expansion to irreversible Vlasov systems (1970). The linearized Vlasov operator supplemented by complete Bhatnagar-Gross-Krook collision integrals as the most important model collision terms is analyzed in detail for a nonrelativistic, nondegenerate, stationary electron gas with neutralizing positive ions and neutral particles without a magnetic field at constant temperature, generalizations for more complex irreversible Vlasov systems being possible. The key of the indirect method given is the introduction of a transformed electron distribution function containing as an additive term an integral over the usual distribution function.     

Distribution function of an electron beam in a focusing magnetic field

The distribution function of electrons moving in an axially symmetric focusing magnetic field is constructed. The macromotion and self-field of the beam are taken into account. The nonrelativistic and relativistic limits are discussed. Upon switching off the magnetic field the distribution functions obtained change into the Maxwell-Boltzmann distribution. The motion of charged particles in a focusing magnetic field is the simplest model for investigation of a beam of particles, for example, electrons, in storage or accelerator rings. In accordance with the well-known theorem of N. Bohr, a magnetic field has no effect on the distribution function for a one-dimensional distribution of electrons with respect to the momenta. However, the situation is altered if macromotion occurs in a static system, for example, the revolution of electrons in storage or accelerator rings. Maintaining the focusing of the beam in an equilibrium orbit, the magnetic field thereby affects the electron distribution function. For an actual electron beam the distribution function is determined by the initial conditions of formation of the beam; however, as a result of scattering processes it will approach some steady-state equilibrium distribution function. We will discuss the problem of finding such a distribution function in the nonrelativistic and relativistic cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 35–40, July, 1978.The author thanks Professor I. M. Ternov of Moscow University for his constant interest in this research and Professor V. G. Bagrov of Tomsk University for help in the research.     

The galaxy-galaxy correlation function as an indicator of critical phenomena in cosmology

We approximate the observable Universe by a collection of equal mass galaxies linked into a many body system by their mutual gravitational interaction. Under the assumptions of (i) nonrelativistic approximation and (ii) global quasi-equilibrium, the partition function of this system can be cast in terms of Ising model spin variables and maps exactly onto a three-dimensional scalar classical field theory. The full machinery of the renormalization group and critical phenomena is brought to bear on this field theory allowing one to calculate the galaxy-to-galaxy correlation function, whose critical exponent is predicted to be between 1.530 to 1.862, to be compared to the phenomenological/observational value of 1.6 to 1.8.     

Relativity stability of quantum gas in a weak magnetic field

Based on the analytical expression of relativistic free energy for a weakly interacting Fermi gas in a weak magnetic field, by using the method of quantum statistics, the stability conditions of the system at both high and low temperatures are given, and the effects of magnetic field and interparticle interactions on the stability of the system are analysed. It is shown that at high temperatures, the stability conditions of the system are completely the same, no matter whether it is the ultrarelativistic case or nonrelativistic case. At extremely low temperatures, the mechanical stability conditions of the system show a similar rule through a comparison between the ultrarelativistic case and nonrelativistic case. At the same time, thermal stability of a relativistic Bose gas in a weak magnetic field is discussed, and the influence of the effect of relativity on the thermal stability of the system is investigated.     

Emission and absorption of neutrinos by nonrelativistic neutrons in a magnetic field

The neutrino luminosity of a nonrelativistic nondegenerate neutron gas in a magnetic field owing to the flip of an anomalous magnetic moment, as well as the mean free path of the neutrino due to the absorption in a magnetized neutron gas, has been calculated using the neutron density matrix in the magnetic field obtained in this work. The Fermi energy and partial concentrations of the degenerate neutron gas in the magnetic field have been determined. The astrophysical applications are discussed.     

Ionization equilibrium of atoms in a strong magnetic field (the saha formula)

The effect of an external magnetic field on the ionization equilibrium of atoms in the nondegenerate nonrelativistic plasma is examined. When taken into account that the interaction of the magnetic moments of electrons with the magnetic field immediately changes their kinetic energy, which is incorrect, the degree of ionization of atoms will increase with increase in the magnetic field strength compared to the atomic concentration in the absence of a magnetic field at the same temperature. When taken into account that this energy changes in view of the Pauli principle and spontaneous minimization of the quantum system, the degree of ionization must decrease with increase in the external magnetic field strength, that is, a strong magnetic field suppresses ionization of atoms in the nonrelativistic plasma at a given temperature. Byelorussian State University; Brest State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 36–39, July, 1999.     

Degenerate Fermi gas of charged particles in a quantizing magnetic field

The strength at which a magnetic field has a quantizing effect on the particles of a degenerate ultrarelativistic electron gas is essentially the same as that for a nonrelativistic proton gas of the same density. Discrete field strengths at which the chemical potentials of these gases have fixed values are expressed in terms of the same index of the Landau quantum level.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 5–9, September, 1991.     

Supersymmetric Quantum Mechanics and SUSY Dependent SU(2) Symmetry for a Spin-1/2 Charged Particle in a Magnetic Field

We find that in a supersymmetric quantum mechanics (SUSY QM) system, in addition to supersymmetric algebra, an associated SU(2) algebra can be obtained by using semiunitary (SUT) operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SU_τ(2) \otimes SU_σ(2) symmetry in the context of the relativistic Pauli Hamiltonian squared. We show that there exists also an SU(2) symmetry associated with the supersymmetry of the Dirac particle.     

Nuclear β-decay and photoproduction of e + e − pairs in intense electromagnetic fields with a complex configuration

The effect of an intense electromagnetic field formed by the superposition of a constant magnetic field and a laser-type field on nuclear β-decay and on pair production by two g-rays with different polarizations is studied. Time integral representations are obtained for the total probabilities of these processes without restrictions on the strengths of the fields making up the configuration. Despite the different nature of these reactions, in the nonrelativistic limitthese expressions contain similar dependences on the field characteristics and the differences reduce to different power-law singularities in the behavior of the integrands at zero. At low fields, complete asymptotic expansions of the probabilities of these processes, including perturbation theory terms and oscillatory field contributions, are obtained in terms of parameters characterizing the fields. It is shown that the oscillatory corrections can be enhanced owing to the effect of a combination external field. The analysis of the probabilities of the various processes given here in terms of nonlinear functions of the field is illustrated by numerical calculations and graphs. Zh. éksp. Teor. Fiz. 113, 21–42 (January 1998)     

On a Phenomenological Approach to Gravity

Applying the theory of sources I consider the consequences of using field theoretical 3- graviton vertex instead of the vertex of general relativity. As an example I look for the lowest nonlinear terms in the exteriormetric of a spherically symmetric body. Themethod suggests that the algorithm of obtaining the metric cannot be reduced to solving the Einstein equation. It also seems that in nonlinear approximation the concept of a test particle moving in external gravitational field can be sustained only for a nonrelativistic particle.     

Novel electric field effects on Landau levels in graphene

A new effect in graphene in the presence of crossed uniform electric and magnetic fields is predicted. Landau levels are shown to be modified in an unexpected fashion by the electric field, leading to a collapse of the spectrum, when the value of electric to magnetic field ratio exceeds a certain critical value. Our theoretical results, strikingly different from the standard 2D electron gas, are explained using a "Lorentz boost," and as an "instability of a relativistic quantum field vacuum." It is a remarkable case of emergent relativistic type phenomena in nonrelativistic graphene. We also discuss few possible experimental consequence.     

Electron Energy Distribution in a Nondegenerate Nonrelativistic Gas Polarized by a Magnetic Field

The effect of a strong magnetic field on the electron energy distribution for a nondegenerate, nonrelativistic magnetized electron gas is assessed in the context of the statistical thermodynamics of equilibrium systems in the general form and for the zero Landau level. The average energy for the level is calculated using the distribution obtained.     

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.     

Derivation of quantum mechanics from the Boltzmann equation for the Planck aether

The Planck aether hypothesis assumes that space is densely filled with an equal number of locally interacting positive and negative Planck masses obeying an exactly nonrelativistic law of motion. The Planck masses can be described by a quantum mechanical two-component nonrelativistic operator field equation having the form of a two-component nonlinear Schrödinger equation, with a spectrum of quasiparticles obeying Lorentz invariance as a dynamic symmetry for energies small compared to the Planck energy. We show that quantum mechanics itself can be derived from the Newtonian mechanics of the Planck aether as an approximate solution of Boltzmann's equation for the locally interacting positive and negative Planck masses, and that the validity of the nonrelativistic Schrödinger equation depends on Lorentz invariance as a dynamic symmetry. We also show how the many-body Schrödinger wave function can be factorized into a product of quasiparticles of the Planck aether with separable quantum potentials. Finally, we present a possible explanation of wave function collapse as a kind of enhanced gravitational collapse in the presence of the negative Planck masses.     

Aharonov-Casher effect and persistent spin currents in a Coulomb-type potential induced by Lorentz symmetry breaking effects

We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field. This neutral particle is also under the influence of a background that breaks the Lorentz symmetry. We focus on the Lorentz symmetry violation background determined by a space-like vector field. Then, we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential. Furthermore, we obtain the bound state solutions to the Schrödinger-Pauli equation and show that the spectrum of energy is a function of the Aharonov-Casher geometric quantum phase. Finally, we discuss the arising of persistent spin currents.     

Approximate energies and thermal properties of a position-dependent mass charged particle under external magnetic fields

We solve the Schr?dinger equation with a position-dependent mass(PDM) charged particle interacted via the superposition of the Morse-plus-Coulomb potentials and is under the influence of external magnetic and Aharonov–Bohm(AB) flux fields. The nonrelativistic bound state energies together with their wave functions are calculated for two spatially-dependent mass distribution functions. We also study the thermal quantities of such a system. Further, the canonical formalism is used to compute various thermodynamic variables for second choosing mass by using the Gibbs formalism. We give plots for energy states as a function of various physical parameters. The behavior of the internal energy, specific heat, and entropy as functions of temperature and mass density parameter in the inverse-square mass case for different values of magnetic field are shown.     

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.     

Shell structure of the electromagnetic energy density in the presence of a ground-state hydrogen atom

The structure of the energy density of the virtual electromagnetic field surrounding a ground-state hydrogen atom is discussed in the framework of nonrelativistic QED. Both the electric and the magnetic part of this energy density are analysed in terms of a shell structure, similar to that previously proposed for the coarse grained energy density W(r). The physical meaning of this shell structure is discussed. It is suggested that, differently from W(r), the energy density investigated here can be measured experimentally, and it is shown that it is rich of detailed information about the dynamical structure of the source atom.