A. Pérez Martínez

Magnetized strange quark matter and magnetized strange quark stars

Strange quark matter could be found in the core of neutron stars or forming strange quark stars. As is well known, these astrophysical objects are endowed with strong magnetic fields that affect the microscopic properties of matter and modify the macroscopic properties of the system. In this article we study the role of a strong magnetic field in the thermodynamical properties of a magnetized degenerate strange quark gas, taking into account {beta}-equilibrium and charge neutrality. Quarks and electrons interact with the magnetic field via their electric charges and anomalous magnetic moments. In contrast to the magnetic field value of 10{sup 19} G, obtained when anomalous magnetic moments are not taken into account, we find the upper bound B < or approx. 8.6x10{sup 17} G, for the stability of the system. A phase transition could be hidden for fields greater than this value.

Stability window and mass–radius relation for magnetized strange quark stars

The stability of magnetized strange quark matter (MSQM) is investigated within the phenomenological MIT bag model, taking into account the variation of the relevant input parameters, namely, the strange quark mass, the baryon density, the magnetic field and the bag parameter. We obtain that the energy per baryon decreases as the magnetic field increases, and its minimum value at vanishing pressure is lower than the value found for strange quark matter (SQM). This implies that MSQM is more stable than non-magnetized SQM. Furthermore, the stability window of MSQM is found to be wider than the corresponding one of SQM. The mass-radius relation for magnetized strange quark stars is also derived in this framework.

ANISOTROPIC PRESSURES IN VERY DENSE MAGNETIZED MATTER

The problem of anisotropic pressures arising from the spatial symmetry breaking introduced by an external magnetic field in quantum systems is discussed. The role of the conservation of energy and momentum of external fields as well as of systems providing boundary conditions in quantum statistics is considered. The vanishing of the average transverse momentum for an electron–positron system in its Landau ground state, i.e. the vanishing of its transverse pressure, is shown. The situation for the neutron case and strange quark matter (SQM) in β equilibrium is briefly discussed. Thermodynamical relations in external fields as well as the form of the stress tensor in a quantum relativistic medium are obtained. The ferromagnetic symmetry breaking is briefly discussed for very dense matter. It is concluded that stable matter cannot exist for fields greater than B = 1018 G.

Magnetized color flavor locked state and compact stars

Abstract.The stability of the color flavor locked phase in the presence of a strong magnetic field is investigated within the phenomenological MIT bag model, taking into account the variation of the strange quark mass, the baryon density, the magnetic field, as well as the bag and gap parameters. It is found that the minimum value of the energy per baryon in a color flavor locked state at vanishing pressure is lower than the corresponding one for unpaired magnetized strange quark matter and, as the magnetic field increases, the energy per baryon decreases. This implies that magnetized color flavor locked matter is more stable and could become the ground state inside neutron stars. The mass-radius relation for such stars is also studied.The stability of the color flavor locked phase in the presence of a strong magnetic field is investigated within the phenomenological MIT bag model, taking into account the variation of the strange quark mass, the baryon density, the magnetic field, as well as the bag and gap parameters. It is found that the minimum value of the energy per baryon in a color flavor locked state at vanishing pressure is lower than the corresponding one for unpaired magnetized strange quark matter and, as the magnetic field increases, the energy per baryon decreases. This implies that magnetized color flavor locked matter is more stable and could become the ground state inside neutron stars. The mass-radius relation for such stars is also studied.

Insignificance of the anomalous magnetic moment of charged fermions for the equation of state of a magnetized and dense medium

We investigate the effects of the anomalous magnetic moment (AMM) in the equation of state (EoS) of a system of charged fermions at finite density in the presence of a magnetic field. In the region of strong magnetic fields (eB>m^2) the AMM is found from the one-loop fermion self-energy. In contrast to the weak-field AMM found by Schwinger, in the strong magnetic field region the AMM depends on the Landau level and decreases with it. The effects of the AMM in the EoS of a dense medium are investigated at strong and weak fields using the appropriate AMM expression for each case. In contrast with what has been reported in other works, we find that the AMM of charged fermions makes no significant contribution to the EoS at any field value.

Quantum Instability of Magnetized Stellar Objects

The equations of state for degenerate electron and neutron gases are studied in the presence of magnetic fields. After including quantum effects in the investigation of the structural properties of these systems, it is found that some hypermagnetized stars can be unstable according to the criterion of stability of pressures. Highly magnetized white dwarfs should collapse producing a supernova type Ia, while superstrong magnetized neutron stars cannot stand their own magnetic field and must implode, too. A comparison of our results with a set of the available observational data of some compact stars is also presented, and the agreement between this theory and observations is verified.

Quantized Faraday effect in (3+1)-dimensional and (2+1)-dimensional systems

We study Faraday rotation in the quantum relativistic limit. Starting from the photon self-energy in the presence of a constant magnetic field the rotation of the polarization vector of a plane electromagnetic wave which travel along the fermion-antifermion gas is studied. The connection between Faraday Effect and Quantum Hall Effect (QHE) is discussed. The Faraday Effect is also investigated for a massless relativistic (2D+1)-dimensional fermion system which is derived by using the compactification along the dimension parallel to the magnetic field. The Faraday angle shows a quantized behavior as Hall conductivity in two and three dimensions.

Local dynamics and gravitational collapse of a self-gravitating magnetized Fermi gas

We use the Bianchi-I spacetime to study the local dynamics of a magnetized self-gravitating Fermi gas. The set of Einstein–Maxwell field equations for this gas becomes a dynamical system in a 4D phase space. We consider a qualitative study and examine numeric solutions for the degenerate zero temperature case. All dynamic quantities exhibit similar qualitative behavior in the 3D sections of the phase space, with all trajectories reaching a stable attractor whenever the initial expansion scalar H0 is negative. If H0 is positive the trajectories end up in a curvature singularity that can be, depending on initial conditions, isotropic or anisotropic. In particular, if the initial magnetic field intensity is sufficiently large the collapsing singularity will always be anisotropic and pointing in the same direction of the field.

Statistical QED model for relativistic fractional quantum Hall effect

Abstract Following the methods of statistical quantum electrodynamics, a heuristic model for relativistic fractional quantum Hall effect is proposed based on three fundamental assumptions: constancy of the chemical potential, fractional Landau quantum numbers due to anyonic effects, and fractional Fermi-Dirac statistics for anyons. The model explains the well-established experimental fact that the plateau extrema of the quantized conductivity are precisely proportional to the inverse filling factors q p .

RELATIVISTIC QUANTUM HALL CONDUCTIVITY FOR 3D AND 2D ELECTRON PLASMA IN AN EXTERNAL MAGNETIC FIELD

The complete antisymmetric form of the conductivity tensor in the static limit, as well as the expression for the Hall conductivity, is obtained for the relativistic 3D and 2D electron gas in a magnetic field. The non-relativistic 2D limit is also discussed. The typical step form of the 2D Hall conductivity at zero temperature is obtained under the simple hypothesis of constancy of the chemical potential.