Strong Quantizing Magnetic Field Research Articles

Effect of the Landau quantization of electrons on the inner crusts of hot neutron stars

In the present work we study the effects of strongly quantizing magnetic fields and finite temperature on the properties of inner crusts of hot neutron stars. The inner crust of a neutron star contains neutron-rich nuclei arranged in a lattice and embedded in gases of free neutrons and electrons. We describe the system within the Wigner-Seitz (WS) cell approximation. The nuclear energy is calculated using Skyrme model with SkM* interaction. To isolate the properties of nuclei we follow the subtraction procedure presented by Bonche, Levit and Vautherin, within the Thomas-Fermi approximation. We obtain the equilibrium properties of inner crust for various density, temperatures and magnetic fields by minimizing the free energy of the WS cell satisfying the charge neutrality and $\beta-$equilibrium conditions. We infer that at a fixed baryon density and temperature, strong quantizing magnetic field reduces the cell radii, neutron and proton numbers in the cell compared with the field free case. However, the nucleon number in the nucleus increases in presence of magnetic field. The free energy per nucleon also decreases in magnetized inner crust. On the other hand, we find that finite temperature tends to smear out the effects of magnetic field. Our results can be important in the context of $r-$process nucleosynthesis in the binary neutron star mergers.

СПИН-ОРБИТАЛЬНАЯ СВЯЗЬ СПАРЕННЫХ ДВУМЕРНЫХ ЭЛЕКТРОНОВ И ФАКТОР ЗАПОЛНЕНИЯ УРОВНЕЙ ЛАНДАУ В РЕЖИМЕ ДРОБНОГО КВАНТОВОГО ЭФФЕКТА ХОЛЛА

A mechanism for pairing and joining two-dimensional electron clusters in a strong quantizing magnetic field is proposed. The aim of this work is to obtain the dependence of the filling factor on the Landau level number N the resulting spin S and magnetic mL quantum numbers determined by the L-S bond of twodimensional electrons. A contactless method for determining the Landau level filling factor  has been developed. An interpretation of the fractional quantum Hall effect is given.

Shubnikov–de Haas Thermoelectric Field Oscillations in Layered Conductors in the Vicinity of a Topological Lifshits Transition

We have studied the response of a layered conductor with a quasi-two-dimensional electron spectrum and a multisheet Fermi surface (FS) formed by two weakly corrugated cylinders and two planar sheets adjoining these cylinders to nonuniform heating. As a result of action of pressure on the conductor or its doping with impurity atoms, distance Δp between the FS cylinder and planar sheets can be reduced to such an extent that conduction electrons begin roaming over these sheets, tunneling from one FS sheet (cavity) to the other. If a conduction electron can visit several times all FS sheets during its mean free time, its motion in the plane orthogonal to the magnetic field becomes finite. In this case, Shubnikov–de Haas oscillations are excited with a period determined by the closed area circumscribed by the electron during its motion in the magnetic-breakdown trajectory in the momentum space. We have calculated the dependence of the thermoelectric field on the magnitude and orientation of a quite strong quantizing magnetic field. In a magnetic field normal to the layers, the cross sections of the cylindrical part of the FS are equidistant from both FS planar sheets. However, this equidistance is violated even for a small deviation of the field from the normal to the layers by angle ϑ, and, at a certain value ϑk of this angle, the probability of magnetic breakdown to one of the FS planar sheets can be so low that the electron cannot close the magnetic-breakdown trajectory, and its motion over the other planar sheet with a visit to the FS cylindrical part becomes infinite. In this case, the magnetic-breakdown quantum oscillations of magnetization and all kinetic characteristics of the conductor disappear, and their disappearance is repeated periodically with a change in the slope of the magnetic field to the layers as a function of tanϑ.

Bremsstrahlung at Low-Energy Electron–Nucleus Collisions in the Quantizing Magnetic Field. I. Distant Collisions

We analytically calculate the spectral power of bremsstrahlung from a slow electron colliding with motionless nuclei in a strong quantizing magnetic field, in which the energy of the Coulomb interaction between particles at a distance of the order of the Larmor radius exceeds the mechanical energy of the system in absolute value. In this case, the electron motion becomes quasibound in sufficiently close collisions. In this part of research, we consider bremsstrahlung at low frequencies, which is stipulated by distant flybys without quasibound motion: an electron can spread over many Landau levels as a result of the collision, but keeps the direction of its motion along the magnetic field. We prove that the transition from the classical to quantum cyclotron gyration of an electron does not manifest itself in the spectral emission power of the waves with arbitrary polarization at the considered frequencies. This property stems from the fact that the low-frequency emission is due to the longitudinal motion and electric drift in the crossed Coulomb and magnetic fields which remain quasiclassical. Thus, we confirm that the bleaching of the photosphere of a magnetic white dwarf, which was discovered in the classical consideration with respect to collisional absorption of the extraordinary wave (polarized across the external magnetic field), is also preserved in the quantum limit—for stars of this spectral type with the strongest magnetic field.

Thomas-Fermi and Thomas-Fermi-Dirac models in two-dimension – Effect of strong quantizing magnetic field

Using Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) models, we have investigated the properties of electron gas inside two-dimensional (2D) Wigner-Seitz (WS) cells in presence of a strong orthogonal quantizing magnetic field. The electron-electron Coulomb exchange interaction in quasi-2D case is obtained. The exact form of exchange term in 2D is derived making the width of the system tending to zero. Further, using the exchange term, the Thomas-Fermi-Dirac equation in 2D is established. It has been observed that only the ionized WS cell can have finite radius in the Thomas-Fermi model, even in presence of a strong quantizing magnetic field. On the other hand, in the Thomas-Fermi-Dirac model a neutral WS cell can have finite radius.

Electrostatic two-stream instability in Fermi-Dirac plasmas

In this paper the electrostatic two-stream instability is investigated for a large range of plasma number-density using the quantum hydrodynamic model by incorporating the relativistic degeneracy, electron-exchange, quantum diffraction and strong parallel quantizing magnetic field effects. It is found that the electron diffraction effect significantly alters the instability growth rate in a wide range of plasma number density. Two cases of classical and quantum Landau quantization limits are compared and the parametric instability condition is closely inspected. It is remarked that for a given streaming speed the instability is bounded by an upper plasma number-density limit. It is also shown that for a given stream speed there is a maximal growth rate corresponding to specific plasma number-density and perturbation wavelength. Current study can help in better understanding of electron-beam plasma interactions and energy exchange for a wide area of number densities ranging from solid density, inertial confined plasmas, big planetary cores and compact stars. It may also be useful in understanding of electrostatic beam-plasma interactions and origin of large magnitude sustainable electrical currents in super-intense plasmas with critically high magnetic fields such as, pulsars, white dwarf interiors and neutron star crusts.

Estimate of Effective Hole Masses in a Germanium Single Crystal in a Uniform Quantizing Magnetic Field

Within the framework of perturbation theory formulas are derived that estimate effective hole masses in a Ge single crystal in a strong quantizing magnetic field in the vicinity of the point kz = 0 when the magnetic field is oriented along the [001] direction. Values of effective hole masses for some Landau levels (n = 2–6) are calculated.

New Method of Determining the Landau Levels in Narrow-Gap Semiconductors

With the help of mathematical models, the temperature dependence of the density of energy states was determined in a quantizing magnetic field. The influence of the effective mass at the temperature dependence of the density of the energy states in a strong quantizing magnetic field is investigated. The dependence temperature of density of energy states graph is obtained in a strong magnetic field for InSb.

The effects of strong quantizing magnetic fields on the cold emission of electrons from ultramagnetized compact stellar objects

Formalisms for both non-relativistic and relativistic versions of field emission of electrons in the presence of a strong quantizing magnetic field, relevant for strongly magnetized neutron stars or magnetars, are developed. In the non-relativistic scenario, where electrons obey the Schrodinger equation, we have noticed that when Landau levels are populated for electrons in the presence of a strong quantizing magnetic field the transmission probability exactly vanishes unless the electrons are spin-polarized in the opposite direction to the external magnetic field. On the other hand, cold electron emission under the influence of a strong electrostatic field at the poles is totally forbidden from the surfaces of those compact objects for which the surface magnetic field strength is ≫1015 G (in the eventuality that they may exist). Whereas in the relativistic case electrons obey the Dirac equation, the presence of a strong quantizing magnetic field completely forbids the emission of electrons from the surfaces of compact objects if B > 1013 G.

On the crustal matter of magnetars

We have investigated some of the properties of dense sub-nuclear matter at the crustal region (both the outer crust and the inner crust region) of a magnetar. The relativistic version of Thomas-Fermi (TF) model is used in presence of strong quantizing magnetic field for the outer crust matter. The compressed matter in the outer crust, which is a crystal of metallic iron, is replaced by a regular array of spherically symmetric Wigner-Seitz (WS) cells. In the inner crust region, a mixture of iron and heavier neutron rich nuclei along with electrons and free neutrons has been considered. Conventional Harrison-Wheeler (HW) and Bethe-Baym-Pethick (BBP) equation of states are used for the nuclear mass formula. A lot of significant changes in the characteristic properties of dense crustal matter, both at the outer crust and the inner crust, have been observed.

The study of relatively low density stellar matter in presence of strong quantizing magnetic field

The effect of strong quantizing magnetic field on the equation of state of matter at the outer crust region of magnetars is studied. The density of such matter is low enough compared to the matter density at the inner crust or outer core region. Based on the relativistic version of semi-classical Thomas–Fermi–Dirac model in presence of strong quantizing magnetic field a formalism is developed to investigate this specific problem. The equation of state of such low density crustal matter is obtained by replacing the compressed atoms/ions by Wigner–Seitz cells with nonuniform electron density. The results are compared with other possible scenarios. The appearance of Thomas–Fermi induced electric charge within each Wigner–Seitz cell is also discussed.

Chiral properties of the QCD vacuum in ultrastrong magnetic fields: A Nambu-Jona-Lasinio model with a semiclassical approximation

The breaking of chiral symmetry of light quarks at zero temperature in the presence of strong quantizing magnetic field is studied using a Nambu-Jona-Lasinio (NJL) model with a Thomas-Fermi-type semiclassical formalism. It is found that the dynamically generated light quark mass can never become zero if the Landau levels are populated and increases with the increase of magnetic field strength.

Neutron star equation of state and the possibility of complex self-energy in Landau theory of a Fermi liquid in the presence of a strong, quantizing magnetic field

Using a relativistic version of Landau theory of Fermi liquid with $\sigma-\omega$ and $\rho$ mesons exchange, we have obtained an equation of state for dense neutron star matter in presence of strong quantizing magnetic field. It is found that in this scenario the self energies of both neutron and proton components of dense neutron star matter become complex under certain physical conditions. To be more specific, it is observed that in the exchange diagrams of $\sigma$, $\omega$ and neutral $\rho$ transfer processes and in the direct interaction diagram with $\rho_\pm$ transfer reactions, the nucleon self-energies become complex in nature.

Analysis of Electron Energy States in a Thin Quantum Well in a Parallel Magnetic Field

We carry out a preliminary investigation of electron dynamics in a quantum well subject to a uniform magnetic field applied parallel to its walls. To achieve exact expressions for the Green's function and associated dispersion relation, we study the narrow limit of a delta-function well profile. The Dyson equation is solved and the dispersion relation is examined for weak and strong (quantizing) magnetic fields.

Relativistic version of Landau theory of Fermi liquid in presence of strong quantizing magnetic field—an exact formalism

An exact formalism for the relativistic version of Landau theory of Fermi liquid in presence of strong quantizing magnetic field is developed. Both direct and exchange type interactions with scalar and vector coupling cases are considered.

DISTRIBUTION OF EQUILIBRIUM EDGE CURRENTS

The distribution of equilibrium edge current density in 2D system subjected to a strong (quantizing) magnetic field has been studied. The case of half plane in normal magnetic field has been considered. The transition from classical strong magnetic field to ultra-quantum limit has been investigated. We have shown that the edge current density oscillates and decays with distance from the edge. The oscillations have been attributed to the Fermi wavelength of electrons. The additional component of the current smoothly depending on the distance but sensitive to the occupation of Landau levels has been found. The temperature suppression of oscillations has been studied.

ELECTRICAL CONDUCTIVITY AT THE CORE OF A MAGNETAR

An expression for the electrical conductivity at the core of a magnetar is derived using Boltzmann kinetic equation with the relaxation time approximation. The rates for the relevant scattering processes, e.g., electron–electron and electron–proton scattering processes are evaluated in presence of strong quantizing magnetic fields using tree level diagrams. It is found that in the presence of a strong quantizing magnetic field, electrical conductivity behaves like a second rank tensor. However, if the zeroth Landau levels are only level occupied by the charged particles, it again behaves like a scalar of a one-dimensional system.

THOMAS–FERMI–DIRAC MODEL FOR LOW DENSITY STELLAR MATTER IN THE PRESENCE OF A STRONG QUANTIZING MAGNETIC FIELD

The effect of strong quantizing magnetic field on low density stellar matter is investigated using Thomas–Fermi–Dirac (TFD) model. The Wigner–Seitz cell structure is assumed for the low density matter. The significant changes in the properties of such low density matter in presence of strong magnetic fields are discussed. It is seen that the decay time scale for magnetic field decreases by at least two orders of magnitude in such a model calculation.

Can there be a quark matter core in a magnetar?

The effects of a strong quantizing magnetic field on the nucleation of quark matter droplets and on the chemical evolution of a nascent quark phase at the core of a magnetar are investigated. The surface energy of the quark phase diverges logarithmically. As a consequence there cannot be a first order transition to the quark phase. However, a metal-insulator type of second order transition is possible unless the field strength exceeds ${10}^{20}$ G. The study of the chemical evolution of a newborn quark phase shows that in $\ensuremath{\beta}$ equilibrium the system becomes energetically unstable.

Dicke superradiance in a magnetoplasma

We present theoretical results for superradiance, i.e. the collective coherent decay of a radiating system, in a semiconductor heterostructure under a strong quantizing magnetic field. We predict a strong peak (‘Dicke peak’) in the emission intensity as a function of time, which should be observable after a short initial excitation of electrons into the conduction band. This peak has a characteristic dependence on the magnetic field and should be observable on sub-picosecond time scales. Furthermore, pumping of electrons and holes into the systems at a rate T leads to a novel kind of oscillation with frequency ∼ T in the limit of the lowest Landau level.