Bulk properties of a Fermi gas in a magnetic field

Abstract

We calculate the number density, energy density, transverse pressure, longitudinal pressure, and magnetization of an ensemble of spin one-half particles in the presence of a homogenous background magnetic field. The magnetic field direction breaks spherical symmetry causing the pressure transverse to the magnetic field direction to be different than the pressure parallel to it. We present explicit formulae appropriate at zero and finite temperature for both charged and uncharged particles including the effect of the anomalous magnetic moment. We demonstrate that the resulting expressions satisfy the canonical relations, Ω = −P and P ⊥ = P − M B, with M = −∂Ω/∂B being the magnetization of the system. We numerically calculate the resulting pressure anisotropy for a gas of protons and a gas of neutrons and demonstrate that the inclusion of the anomalous magnetic increases the level of pressure anisotropy in both cases.

Effects of strong magnetic fields on hybrid stars

“…The magnetization is defined as M = −∂ Ω/∂ B (for more details see [33]) and in Figure 1 we show: i) the case when the magnetic field is included only in the structure of the star (no EoS(B), no mag); ii) the effect of the magnetic field also into the equation of state on the neutron star structure without the magnetization term (EoS(B), no mag) and iii) the effect of the magnetic field also into the equation of state on the neutron star structure plus the magnetization term (EoS(B), mag). We also show the non-magnetized cased denominated TOV.…”

Protoquark stars: stability windows and magnetic field effects

“…On the other hand, the QMDD model can successfully describe these stars, even if they are not magnetars. Finally we have chosen the MIT bag model and reobtained its EOS through an anisotropic energy momentum tensor [8]. Due to the magnetic field, the perpendicular component of the matter contribution to the pressure is modified.…”

One-loop QCD thermodynamics in a strong homogeneous and static magnetic field

“…Since the magnetic field breaks the translational invariance of space, so the pressure becomes anisotropic arising due to the difference between the pressures, which are transverse and longitudinal to the direction of background magnetic field, which is illustrated in an ensemble of spin one-half particles [24]. Recently the lattice QCD simulations [36] have explored the effects of background magnetic fields on the equation of state (EoS) by calculating the thermodynamic observables, namely the transverse and longitudinal pressures, the magnetization, the energy density, the entropy density etc.…”

“…Moreover the magnetic field may be assumed uniform because even though the spatial distribution of the magnetic field is globally inhomogeneous, but in the central region of the overlapping nuclei, the magnetic field in the transverse plane varies very smoothly, which is noticed in the hadron-string simulations [9] for Au-Au collisions at √ s N N = 200 GeV with an impact parameter, b = 10 fm. Therefore, a large number of QCD related phenomena are investigated in the strong and homogeneous magnetic field, such as the chiral magnetic effect related to the generation of electric current parallel to the magnetic field due to the difference in number of right and left-handed quarks [10][11][12], the axial magnetic effect due to the flow of energy by the axial magnetic field [13,14], the chiral vortical effect due to an effective magnetic field in the rotating QGP [15,16], the magnetic catalysis and the inverse magnetic catalysis at finite temperature arising due to the breaking and the restoration of the chiral symmetry [17][18][19][20][21], the thermodynamic properties [22][23][24], the refractive indices and decay constant [25,26] of mesons in a hot magnetized medium, the conformal anomaly and the production of soft photons [27,28] at RHIC and LHC, the dispersion relation in a magnetized thermal QED [29], the synchrotron radiation [30], the dilepton production from both the weakly [31][32][33][34] and the strongly [35] coupled plasma etc.…”