Equilibrium of a Degenerate Gas of Nucleons and Electrons in a Strong Magnetic Field

A model of a degenerate ideal gas of nucleons and electrons in a superstrong magnetic field is used to describe the state of matter in the central region of a strongly magnetized neutron star. The influence of a constant uniform superstrong magnetic field on the equilibrium conditions and the equation of state for the degenerate gas of neutrons, protons, and electrons is investigated in the framework of this model. The contribution determined by the interaction of the anomalous magnetic moments of the fermions with the magnetic field is taken into account. The influence of the superstrong magnetic field on the process of gravitational collapse of a magnetized neutron star is discussed under the assumption that the central region of the star consists mostly of degenerate neutrons. We show that if the densities of electrons, protons, and neutrons are relatively low depending on the field strength, the fermion gases in a superstrong uniform magnetic field become totally polarized with respect to the spin. We discuss the possibility of spontaneous magnetization occurring in a system of degenerate neutrons where the exchange interaction effects are taken into account.     

Electroweak Nucleon Decays in a Superstrong Magnetic Field

We study the influence of a magnetic field on the electroweak processes of nucleon decay in a degenerate ideal gas of neutrons, protons, and electrons situated in an external superstrong constant and homogeneous magnetic field with effects due to the interaction of nucleon anomalous magnetic moments with the magnetic field taken into account. For different values of the chemical potentials of degenerate fermions, we obtain expressions for probabilities of electroweak processes, which are assumed to be responsible for the chemical equilibrium in the central domain of a neutron star with a frozen superstrong magnetic field. We show that the difference between the neutron decay probabilities in the presence of a magnetic field B ≪ 10¹⁷ G and without this field is completely determined by changing the phase volume of electron states. We discuss the process of proton decay into a neutron, positron, and neutrino. This process is energetically allowed only when the interaction of nucleon anomalous magnetic moments with a superstrong magnetic field is taken into account. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 1, pp. 108–122, October, 2005.     

Nucleon Instability in a Degenerate Magnetized Nucleon–Electron Gas

In the framework of the model of a degenerate relativistic ideal neutron–proton–electron gas (np ⁺ e ^– gas) in an external superstrong constant and homogeneous magnetic field, we study the effect of the magnetic field on the state of chemical equilibrium of the np ⁺ e ^– gas and on the processes of electronic (^–) and positronic (⁺) nucleon decay taking the effects due to the interaction between the nucleon anomalous magnetic moments and the magnetic field into account. For sufficiently large values of the magnetic induction, the proton density in chemical equilibrium must exceed the neutron density. Including the interaction between the nucleon anomalous magnetic moments M _n,p and the magnetic field results in an insignificant reduction of the proton density, but, as in the case M _n,p=0, the proton density in chemical equilibrium in the presence of the superstrong magnetic field exceeds the neutron density. We show that if the interaction between the nucleon anomalous magnetic moments and the superstrong magnetic field is taken into account, then the positronic decay of a free proton (i.e., a proton not entering the composition of an atomic nucleus) into a neutron, a positron, and a neutrino can become energetically allowed. We discuss the necessary conditions for realizing the phase transition from the nucleon phase to the quark phase of the substance in the central region of a strongly magnetized neutron star.     

Neutral Fermion with a Magnetic Moment in External Electromagnetic Fields

The interaction between a massive neutral fermion with a static (spin) magnetic dipole moment and an external electromagnetic field is described by the Dirac–Pauli equation. Exact solutions of this equation are obtained along with the corresponding energy spectrum for an axially symmetric external magnetic field and for some centrally symmetric electric fields. It is shown that the spin–orbital interaction of a neutral fermion with a magnetic moment determines both the characteristic properties of the quantum states and the fermion energy spectrum. It is found that (1) the discrete energy spectrum of a neutral fermion depends on the projection of the fermion spin on a certain quantization axis, (2) the ground energy level of a fermion in these electric fields as well as the energy levels of all bound states with a fixed value of the quantum number characterizing the projection of the fermion spin in the electric field E = er is degenerate and the degeneration order is countably infinite, and (3) the energy spectra of neutral fermions and antifermions with spin magnetic moments are symmetric in centrally symmetric fields. Bound states of a neutral fermion with a magnetic moment in an external electric field do exist even if the Dirac–Pauli equation does not explicitly contain the term with the fermion mass. In addition, in centrally symmetric electric fields, there exist a countably infinite set of pairs of isolated charge-conjugate zero-energy solutions of the Dirac–Pauli equation.     

Nonlinear Electromagnetic Delay of Electromagnetic Signals Propagating in the Magnetic Meridian Plane of Pulsars and Magnetars

We analyze the propagation of electromagnetic waves in the magnetic meridian planes of neutron stars with a strong magnetic field in the framework of the parameterized post-Maxwellian electrodynamics of the vacuum. The origin of these electromagnetic waves is the curvature emission of X-rays and gamma rays from high-energy electrons in the vicinity of the magnetic poles of neutron stars. We show that in the case of a slowly varying intensity of X-ray and gamma-ray emission, the delay of the slow normal mode of electromagnetic waves relative to the fast mode results in a shift of the time dependence of the intensity of the detected radiation with one polarization relative to that of the radiation with the orthogonal polarization. In the case of single X-ray or gamma-ray pulses, the delay effect results in the polarization of the detected pulse varying during the pulse length, the leading edge of all pulses being polarized normally to the magnetic equator plane of the neutron star. We note that the modern level of the experimental technique, in principle, allows observing the manifestations of the delay effect for signals of different polarizations.     

The effects of strong magnetic fields and rotation on soliton stars at finite temperature

We study the effects of strong magnetic fields and uniform rotation on the properties of soliton stars in Lee-Wick model when a temperature dependence is introduced into this model. We first recall the properties of the Lee-Wick model and study the properties of soliton solutions, in particular, the stability condition, in terms of the parameters of the model and in terms of the number of fermions N inside the soliton (for very large N) in the presence of strong magnetic fields and uniform rotation. We also calculate the effects of gravity on the stability properties of the soliton stars in the simple approximation of coupling the Newtonian gravitational field to the energy density inside the soliton, treating this as constant throughout. Following Cottingham and Vinh Mau, we also make an analysis at finite temperature and show the possibility of a phase transition which leads to a model with parameters similar to those considered by Lee and his colleagues but in the presence of magnetic fields and rotation. More specifically, the effects of magnetic fields and rotation on the soliton mass and transition temperature are computed explicitly. We finally study the evolution on these magnetized and rotating soliton stars with the temperature from the early universe to the present time.     

Neutral Fermion Having Electric and Magnetic Moments in an External Electromagnetic Field

We show that in 2+1 dimensions, the Dirac equation for a neutral fermion possessing electric and magnetic dipole moments in an external electromagnetic field reduces to the Dirac equation for a charged fermion in a external field characterized by a certain 3-pseudo-vector potential. The effective charge of the neutral fermion is determined by its dipole moments. The effects of coupling electric and magnetic moments of the neutral fermion to the external electromagnetic field seem to be inseparable in physical experiments of any type. We find an exact solution of the Dirac equation for a massive neutral fermion with electric and magnetic dipole moments in a external plane-wave electromagnetic field. We derive expressions for the fermionic vacuum current induced by neutral fermions in the presence of external electromagnetic fields.     

On the motion of a solid in a magnetic field

The problem of the motion of a magnetic solid in a constant uniform magnetic field, taking gyromagnetic effects into account, is considered. The equations of motion are derived, the Hamiltonian structure is studied, and the cases of integrability indicated. Certain classes of stationary motions are studied and their stability examined.

The gyromagnetic effects arise because the electrons have magnetic and mechanical spin moments /1/. The rotation of the body causes it to become magnetized (the Barnett effect) and when a freely suspended body is magnetized, it begins to rotate (the Einsteinde Haas effect). It is found that gyromagnetic phenomena must be taken into account when analysing the motion of gyroscopic precision systems.     

Pauli isotonic oscillatorwith an anomalous magnetic moment in the presence of the Aharonov–Bohm effect: Laplace transform approach

A strong magnetic field significantly affects the intrinsic magnetic moment of fermions. In quantum electrodynamics, it was shown that the anomalous magnetic moment of an electron arises kinematically, while it results from a dynamical interaction with an external magnetic field for hadrons (proton). Taking the anomalous magnetic moment of a fermion into account, we find an exact expression for the boundstate energy and the corresponding eigenfunctions of a two-dimensional nonrelativistic spin-1/2 harmonic oscillator with a centripetal barrier (known as the isotonic oscillator) including an Aharonov–Bohm term in the presence of a strong magnetic field. We use the Laplace transform method in the calculations. We find that the singular solution contributes to the phase of the wave function at the origin and the phase depends on the spin and magnetic flux.     

Scattering of a neutral fermion with anomalous magnetic moment by a charged straight thin thread

We consider the scattering of a massive neutral fermion with an anomalous magnetic moment in the electric field of a homogeneously charged straight thin thread from the standpoint of the quantum mechanical problem of constructing a self-adjoint Hamiltonian for the nonrelativistic Dirac-Pauli equation. Using the solutions obtained for the self-adjoint Hamiltonian, we investigate the scattering of the neutral fermion in the electric field of a thread oriented perpendicular to the plane of fermion motion (the Aharonov-Casher effect). We find expressions for the scattering amplitude and cross section of neutral fermions in the electric field of the thread. We show that the scattering amplitude and cross section depend both on the direct interaction between the fermion anomalous magnetic moment and the electric field and on the polarization of the fermionic beam in the initial state.     

Why do the microstructures of the main pulse and the interpulse of the pulsar in the Crab nebula differ so dramatically?

Theoretical and Mathematical Physics - Pulsars are magnetized neutron stars. They are not resolved by modern radio telescopes and are studied only by radiation coming from the regions of the...     

Microscopic Quantum Hydrodynamics of Systems of Fermions: Part I

The fundamental equations of the microscopic quantum hydrodynamics of fermions in an external electromagnetic field (i.e., the particle balance equation, the momentum balance equation, the energy balance equation, and the magnetic moment balance equation) are derived using the Schrödinger equation. The form of the spin–spin interaction Hamiltonian is specified. To close the system of the balance equations for a multiparticle fermion system, the effective one-particle Schrödinger equation must be introduced.     

Properties of the heavy-fermion spectrum in the canted phase of antiferromagnetic intermetallides

We study the effect of the magnetic-field-induced canting of magnetic sublattices on the energy structure of heavy fermion quasiparticles in intermetallides with antiferromagnetic-type ordering. We work in the framework of an effective Hamiltonian of the periodic Anderson model in the regime of strong electron correlations. With the virtual transfers into high-energy double states taken into account, this Hamiltonian involves exchange interactions between spin moments of the f ions and the s-f-exchange coupling between the two subsystems. For a noncollinear problem geometry, we introduce a unitary transformation that allows reducing an eighth-order equation for the spectrum of heavy fermions to two fourth-order equations. We show that the quasimomentum dependence of the heavy-fermion energy changes qualitatively under the transition from the antiferromagnetic phase to a phase with a considerable canting angle emerging in an external magnetic field.     

Stability of Quantum Electrodynamics and Quantum Chromodynamics

We consider the vacuum energy in QED viewed as in a system of charged fermions and bosons and in QCD viewed as in a system of quarks (fermions) and gluons (bosons) in a self-dual field with a constant strength. We show that the cause of instability is the instability of bosons in the self-dual vacuum field. For the global stability of a system consisting of fermions and bosons, the number of fermions should be sufficiently large. The nonzero self-dual field leading to the confinement of fermions realizes the minimum of the vacuum energy in the case where the boson has the smallest mass in the system. Confinement therefore does not arise in QED, where the fermion (electron) has the smallest mass, and does arise in QCD, where the boson (gluon) has the smallest mass.     

Scattering theory for a class of fermionic Pauli-Fierz models

The scattering theory for a class of fermionic Pauli-Fierz models is considered. We give a proof of the asymptotic completeness of the dynamics in the case of massive fermions. The result applied to the Hamiltonian of a quantized spin- Dirac particle interacting with an external field through a cutoff Yukawa interaction and to the Hamiltonian of a system of finitely many confined particles coupled to a fermionic field with a quadratic interaction.     

Computing the Particle Paths in an Open-Trap Sharp-Point Geometry

The article presents simulation results for the motion of electrons in two different regions: a high-current vacuum diode and an open trap. The entire system is immersed in an external magnetic field with sharp-point geometry. The electrons are continuously injected from a part of the cathode into the diode region, where they are accelerated to relativistic velocities. In this region, the self-consistent problem of particle motion in electromagnetic fields is solved by the large particle method. In the magnetic trap region, the particles experience only the external magnetic field, and their paths are computed by the test particle method. The simulation efficiency is improved by partitioning the problem into two: separate simulation of the high-voltage diode and integration of the particle paths in the trap. Calculations show that the bulk of the particles leave the trap through the side walls, moving along the magnetic forcelines, and only a small part of the particles undergo multiple reflections and remain longer inside the trap.     

Uniform Lieb-Thirring Inequality for the Three-Dimensional Pauli Operator with a Strong Non-Homogeneous Magnetic Field

The Pauli operator describes the energy of a nonrelativistic quantum particle with spin in a magnetic field and an external potential. A new Lieb- Thirring type inequality on the sum of the negative eigenvalues is presented. The main feature compared to earlier results is that in the large field regime the present estimate grows with the optimal (first) power of the strength of the magnetic field. As a byproduct of the method, we also obtain an optimal upper bound on the pointwise density of zero energy eigenfunctions of the Dirac operator. The main technical tools are: (i) a new localization scheme for the square of the resolvent of a general class of second order elliptic operators; (ii) a geometric construction of a Dirac operator with a constant magnetic field that approximates the original Dirac operator in a tubular neighborhood of a fixed field line. The errors may depend on the regularity of the magnetic field but they are uniform in the field strength. Communicated by Gian Michele GrafSubmitted 31/08/03, accepted 28/01/04     

Proton magnetic resonance in coumarins

The high resolution proton magnetic resonance spectra of AB, ABC and ABCD systems in fourteen coumarins have been studied. Chemical shifts and spin coupling constants for the protons in various positions in the benzo-α-pyrone ring have been obtained. The spectrum of coumarin confirms the ethylenic nature of double bond between carbon atoms in positions 3 and 4. The chemical shifts for the phenyl protons are in conformity with the reactivities of the coumarins at various positions in the ring. A linear relation has been observed between the chemical shift for proton in 8 position in various 6 substituted coumarins and the Hammett’s constants (σ) for substituents in themeta position. The NMR spectra offer a very convenient method for distinguishing between 3 and 4 substituted coumarins on account of the large chemical shift for the protons in positions 3 and 4. The results do not substantiate resonance of the naphthalene type in coumarin as suggested to explain its dipole moment.     

Hybrid Simulation of Space Plasmas: Models with Massless Fluid Representation of Electrons. IV. Kelvin–Helmholtz Instability

This is a survey of the literature on hybrid simulation of the Kelvin–Helmholtz instability. We start with a brief review of the theory: the simplest model of the instability—a transition layer in the form of a tangential discontinuity; compressibility of the medium; finite size of the velocity shear region; pressure anisotropy. We then describe the electromagnetic hybrid model (ions as particles and electrons as a massless fluid) and the main numerical schemes. We review the studies on two-dimensional and three-dimensional hybrid simulation of the process of particle mixing across the magnetopause shear layer driven by the onset of a Kelvin–Helmholtz instability. The article concludes with a survey of literature on hybrid simulation of the Kelvin–Helmholtz instability in finite-size objects: jets moving across the magnetic field in the middle of the field reversal layer; interaction between a magnetized plasma flow and a cylindrical plasma source with zero own magnetic field.