Matter In Strong Magnetic Fields Research Articles

Thermal effect in hot QCD matter in strong magnetic fields

Thermal effect in hot QCD matter in strong magnetic fields

Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice

QCD matter in strong magnetic field exhibits a rich phase structure. In the presence of an external magnetic field, the chiral Lagrangian for two flavors is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous coupling of the neutral pion π0 to the magnetic field via the chiral anomaly. Due to this term, the ground state is inhomogeneous in the form of either chiral soliton lattice (CSL), an array of solitons in the direction of magnetic field, or domain-wall Skyrmion (DWSk) phase in which Skyrmions supported by π3[SU(2)] ≃ ℤ appear inside the solitons as topological lumps supported by π2(S2) ≃ ℤ in the effective worldvolume theory of the soliton. In this paper, we determine the phase boundary between the CSL and DWSk phases beyond the single-soliton approximation, within the leading order of chiral perturbation theory. To this end, we explore a domain-wall Skyrmion chain in multiple soliton configurations. First, we construct the effective theory of the CSL by the moduli approximation, and obtain the ℂP1 model or O(3) model, gauged by a background electromagnetic gauge field, with two kinds of topological terms coming from the WZW term: one is the topological lump charge in 2+1 dimensional worldvolume and the other is a topological term counting the soliton number. Topological lumps in the 2+1 dimensional worldvolume theory are superconducting rings and their sizes are constrained by the flux quantization condition. The negative energy condition of the lumps yields the phase boundary between the CSL and DWSk phases. We find that a large region inside the CSL is occupied by the DWSk phase, and that the CSL remains metastable in the DWSk phase in the vicinity of the phase boundary.

Searching optimum equations of state of neutron star matter in strong magnetic fields with rotation

Abstract Masses and radii of neutron stars are obtained in the presence of strong magnetic fields together with rotation. Mass-radius relations are calculated using 11 equations of state (EoSs: GM1, TM1-a, TM1-b, TM2$\omega\rho$-a, TM2$\omega\rho$-b, NL3-a, NL3-b, NL3$\omega\rho$-a, NL3$\omega\rho$-b, DDME2-a and DDME2-b) in relativistic mean field (RMF) theory. Obtained masses are over and around twice the solar mass ($M_\odot$) for all EoSs in the presence of strong magnetic fields of $3 \times 10^{18}$ G at the center. For NL3$\omega\rho$-a and NL3$\omega\rho$-b EoSs, masses are more than $M=2.17\,M_\odot$(observed maximum mass: $2.14\,M_\odot$) even without magnetic fields. Rotational effects are found to be insignificant in any case, at least up to the Kepler frequency. Suitable EoSs are also selected concerning the constraint on the radius of a neutron star.

Chiral symmetry breaking, color superconductivity, and equation of state for magnetized strange quark matter

We investigate the vacuum structure of dense quark matter in strong magnetic fields at finite temperature and densities in a 3 flavor Nambu Jona Lasinio (NJL) model including the Kobayashi-Maskawa-t'Hooft (KMT) determinant term using a variational method. The method uses an explicit structure for the `ground' state in terms of quark-antiquark condensates as well as diquark condensates. The mass gap equations and the superconducting gap equations are solved self consistently and are used to compute the thermodynamic potential along with the charge neutrality conditions. We also derive the equation of state for the charge neutral strange quark matter in the presence of strong magnetic fields which could be relevant for neutron stars.

Anomalous electrodynamics of neutral pion matter in strong magnetic fields

The ground state of quantum chromodynamics in sufficiently strong external magnetic fields and at moderate baryon chemical potential is a chiral soliton lattice (CSL) of neutral pions [1]. We investigate the interplay between the CSL structure and dynamical electromagnetic fields. Our main result is that in presence of the CSL background, the two physical photon polarizations and the neutral pion mix, giving rise to two gapped excitations and one gapless mode with a nonrelativistic dispersion relation. The nature of this mode depends on the direction of its propagation, interpolating between a circularly polarized electromagnetic wave [2] and a neutral pion surface wave, which in turn arises from the spontaneously broken translation invariance. Quite remarkably, there is a neutral-pion-like mode that remains gapped even in the chiral limit, in seeming contradiction to the Goldstone theorem. Finally, we have a first look at the effect of thermal fluctuations of the CSL, showing that even the soft nonrelativistic excitation does not lead to the Landau-Peierls instability. However, it leads to an anomalous contribution to pressure that scales with temperature and magnetic field as T5/2(B/fπ )3/2.

Phase diagram of QCD in a magnetic field

We review in detail recent advances in our understanding of the phase structure and the phase transitions of hadronic matter in strong magnetic fields B and zero quark chemical potentials µf. Many aspects of QCD are described using low-energy effective theories and models such as the MIT bag model, the hadron resonance gas model, chiral perturbation theory, the Nambu-Jona-Lasinio (NJL) model, the quark-meson (QM) model and Polyakov-loop extended versions of the NJL and QM models. We critically examine their properties and applications. This includes mean-field calculations as well as approaches beyond the mean-field approximation such as the functional renormalization group (FRG). Renormalization issues are discussed and the influence of the vacuum fluctuations on the chiral phase transition is pointed out. Magnetic catalysis at T = 0 is covered as well. We discuss recent lattice results for the thermodynamics of nonabelian gauge theories with emphasis on SU(2)c and SU(3)c. In particular, we focus on inverse magnetic catalysis around the transition temperature Tc as a competition between contributions from valence quarks and sea quarks resulting in a decrease of Tc as a function of B. Finally, we discuss recent efforts to modify models in order to reproduce the behavior observed on the lattice.

Dense matter in strong magnetic fields

Compact stars having strong magnetic fields (magnetars) have been observationally determined to have surface magnetic fields of order of 1014 – 1015 G, the implied internal field strength being several orders larger. We study the equation of state and composition of hypernuclear matter and quark matter - two forms of dense matter in strong magnetic fields. We find that the magnetic field has substantial influence on the properties of hypernuclear matter and quark matter for magnetic field B ≥ 1017 G and B ≥ 1018 G respectively. In particular the matter properties become anisotropic. Moreover, above a critical field Bcr, both hypernuclear and quark matter show instability, although the values of Bcr are different for two kinds of matter.

Strange quark matter in strong magnetic fields within a confining model

We construct an equation of state of strange quark matter in a strong magnetic field within a confining model. The confinement is modeled by means of the Richardson potential for quark-quark interaction modified suitably to account for a strong magnetic field. We compare our results for the equation of state and magnetization of matter to those derived within the MIT bag model. The differences between these models arise mainly due to the momentum dependence of the strong interaction between quarks in the Richardson model. Specifically, we find that the magnetization of strange quark matter in this model has much more pronounced de Haas-van Alfv\'en oscillations than in the MIT bag model, which is the consequence of the (static) gluon-exchange structure of the confining potential.

Saturated symmetric nuclear matter in strong magnetic fields

Strongly magnetized symmetric nuclear matter is investigated within the context of effective baryon-meson exchange models. The magnetic field is coupled to the charge as well as the dipole moment of the baryons by including the appropriate terms in the Lagrangian density. The saturation density of magnetized, symmetric nuclear matter was calculated for magnetic fields of the order of 10^17 gauss. For the calculated range of saturation densities the binding energy, symmetry energy coefficient and compressibility of nuclear matter were also calculated. It is found that with an increasing magnetic field the saturation density increases, while the system becomes less bound. Furthermore, the depopulation of proton Landau levels leaves a distinct fluctuating imprint on the symmetry energy coefficient and compressibility. The calculations were also performed for increased values of the baryon magnetic dipole moment. By increasing the dipole moment strength the saturation density is found to decrease, but the system becomes more tightly bound while the fluctuations in the symmetry energy coefficient and compressibility persist.

Anisotropic pressure in strange quark matter in the presence of a strong magnetic field

The thermodynamic properties of strange quark matter in strong magnetic fields H up to 1020 G are considered within the MIT bag model at zero temperature implying the constraints of total baryon number conservation, charge neutrality and chemical equilibrium. The pressure anisotropy, exhibited in the difference between the pressures along and perpendicular to the field direction, becomes essential at H > Hth, with the estimate 1017 < Hth ≲ 1018 G. The longitudinal pressure vanishes at the critical field Hc, which can be somewhat smaller or larger than 1018 G depending on the total baryon number density and bag pressure. As a result, longitudinal instability occurs in strange quark matter, which precludes: (1) a significant drop in the content of s quarks, which, otherwise could happen at H ∼ 1020 G; (2) the appearance of positrons in weak processes in a narrow interval near H ∼ 2 × 1019 G (replacing electrons). The occurrence of the longitudinal instability leaves the possibility only for electrons to reach a fully polarized state, while for all quark flavors the polarization remains mild even for fields near Hc. The anisotropic equation of state is determined under the conditions relevant to the interiors of magnetars.

Hypernuclear matter in strong magnetic field

Compact stars with strong magnetic fields (magnetars) have been observationally determined to have surface magnetic fields of order of 10^{14}-10^{15} G, the implied internal field strength being several orders larger. We study the equation of state and composition of dense hypernuclear matter in strong magnetic fields in a range expected in the interiors of magnetars. Within the non-linear Boguta-Bodmer-Walecka model we find that the magnetic field has sizable influence on the properties of matter for central magnetic field B \ge 10^{17} G, in particular the matter properties become anisotropic. Moreover, for the central fields B \ge 10^{18} G, the magnetized hypernuclear matter shows instability, which is signaled by the negative sign of the derivative of the pressure parallel to the field with respect to the density, and leads to vanishing parallel pressure at the critical value B_{\rm cr} \simeq 10^{19} G. This limits the range of admissible homogeneously distributed fields in magnetars to fields below the critical value B_{\rm cr}.

Dressed Polyakov loop and phase diagram of hot quark matter in a magnetic field

We evaluate the dressed Polyakov loop for hot quark matter in strong magnetic field. To compute the finite temperature effective potential, we use the Polyakov extended Nambu-Jona Lasinio model with eight-quark interactions taken into account. The bare quark mass is adjusted in order to reproduce the physical value of the vacuum pion mass. Our results show that the dressed Polyakov loop is very sensitive to the strenght of the magnetic field, and it is capable to capture both the deconfinement crossover and the chiral crossover. Besides, we compute self-consistently the phase diagram of the model. We find a tiny split of the two aforementioned crossovers as the strength of the magnetic field is increased. Concretely, for the largest value of magnetic field investigated here, $eB=19 m_\pi^2$, the split is of the order of $10\%$. A qualitative comparison with other effective models and recent Lattice results is also performed.

Spin-polarized states in neutron matter in a strong magnetic field

Spin-polarized states in neutron matter in strong magnetic fields up to ${10}^{18}$ G are considered in the model with the Skyrme effective interaction. By analyzing the self-consistent equations at zero temperature, it is shown that a thermodynamically stable branch of solutions for the spin-polarization parameter as a function of density corresponds to the negative spin polarization when the majority of neutron spins are oriented opposite to the direction of the magnetic field. Besides, beginning from some threshold density dependent on magnetic field strength, the self-consistent equations also have two other branches of solutions for the spin-polarization parameter with the positive spin polarization. The free energy corresponding to one of these branches turns out to be very close to that of the thermodynamically preferable branch. As a consequence, in a strong magnetic field, the state with the positive spin polarization can be realized as a metastable state in the high-density region in neutron matter, which, under decreasing density, at some threshold density changes to a thermodynamically stable state with the negative spin polarization.

Properties of hyperonic matter in strong magnetic fields

We study the effects of strong magnetic fields on the properties of hyperonic matter. We employ the relativistic mean field theory, which is known to provide excellent descriptions of nuclear matter and finite nuclei. The two additional hidden-strangeness mesons, ${\ensuremath{\sigma}}^{*}$ and \ensuremath{\phi}, are taken into account, and some reasonable hyperon potentials are used to constrain the meson-hyperon couplings, which reflect the recent developments in hypernuclear physics. It is found that the effects of strong magnetic fields become significant only for magnetic field strength $B&gt;5\ifmmode\times\else\texttimes\fi{}{10}^{18}$ G. The threshold densities of hyperons can be significantly altered by strong magnetic fields. The presence of hyperons makes the equation of state (EOS) softer than that in the case without hyperons, and the softening of the EOS becomes less pronounced with increasing magnetic field strength.

Pulsar kicks by anisotropic neutrino emission from quark matter in strong magnetic fields

Aims. We critically discuss a pulsar acceleration mechanism based on asymmetric neutrino emission from the direct quark Urca process in the interior of proto neutron stars.

Cohesive property of magnetized neutron star surfaces: Computations and implications

The cohesive energy of condensed matter in strong magnetic fields is a fundamental quantity characterizing magnetized neutron star surfaces. The cohesive energy refers to the energy required to pull an atom out of the bulk condensed matter at zero pressure. Theoretical models of pulsar and magnetar magnetospheres depend on the cohesive properties of the surface matter in strong magnetic fields. For example, depending on the cohesive energy of the surface matter, an acceleration zone (“polar gap”) above the polar cap of a pulsar may or may not form. Also, condensation of the neutron star surface, if it occurs, can significantly affect thermal emission from isolated neutron stars. We describe our calculations of the cohesive property of matter in strong magnetic fields, and discuss the implications of our results to the recent observations of neutron star surface emission as well as to the detection/non-detection of radio emission from magnetars.

Density-functional-theory calculations of matter in strong magnetic fields. II. Infinite chains and condensed matter

We present calculations of the electronic structure of one-dimensional infinite chains and three-dimensional condensed matter in strong magnetic fields ranging from $B={10}^{12}\phantom{\rule{0.3em}{0ex}}\mathrm{G}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}2\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.3em}{0ex}}\mathrm{G}$, appropriate for observed magnetic neutron stars. At these field strengths, the magnetic forces on the electrons dominate over the Coulomb forces, and to a good approximation the electrons are confined to the ground Landau level. Our calculations are based on the density functional theory, and use a local magnetic exchange-correlation function appropriate in the strong field regime. The band structures of electrons in different Landau orbitals are computed self-consistently. Numerical results of the ground-state energies and electron work functions are given for one-dimensional chains ${\mathrm{H}}_{\ensuremath{\infty}}$, ${\mathrm{He}}_{\ensuremath{\infty}}$, ${\mathrm{C}}_{\ensuremath{\infty}}$, and ${\mathrm{Fe}}_{\ensuremath{\infty}}$. Fitting formulae for the $B$ dependence of the energies are also provided. For all the field strengths considered in this paper, hydrogen, helium, and carbon chains are found to be bound relative to individual atoms (although for $B$ less than a few $\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.3em}{0ex}}\mathrm{G}$, carbon infinite chains are very weakly bound relative to individual atoms). Iron chains are significantly bound for $B\ensuremath{\gtrsim}{10}^{14}\phantom{\rule{0.3em}{0ex}}\mathrm{G}$ and are weakly bound if at all at $B\ensuremath{\lesssim}{10}^{13}\phantom{\rule{0.3em}{0ex}}\mathrm{G}$. We also study the cohesive property of three-dimensional condensed matter of H, He, C, and Fe at zero pressure, constructed from interacting chains in a body-centered tetragonal lattice. Such three-dimensional condensed matter is found to be bound relative to individual atoms, with the cohesive energy increasing rapidly with increasing $B$.

Density-functional-theory calculations of matter in strong magnetic fields. I. Atoms and molecules

We present calculations of the electronic structure of various atoms and molecules in strong magnetic fields ranging from $B={10}^{12}\phantom{\rule{0.3em}{0ex}}\mathrm{G}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}2\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.3em}{0ex}}\mathrm{G}$, appropriate for radio pulsars and magnetars. For these field strengths, the magnetic forces on the electrons dominate over the Coulomb forces, and to a good approximation the electrons are confined to the ground Landau level. Our calculations are based on the density functional theory, and use a local magnetic exchange-correlation function which is tested to be reliable in the strong field regime. Numerical results of the ground-state energies are given for ${\mathrm{H}}_{N}$ (up to $N=10$), ${\mathrm{He}}_{N}$ (up to $N=8$), ${\mathrm{C}}_{N}$ (up to $N=5$), and ${\mathrm{Fe}}_{N}$ (up to $N=3$), as well as for various ionized atoms. Fitting formulae for the $B$ dependence of the energies are also given. In general, as $N$ increases, the binding energy per atom in a molecule, $\ensuremath{\mid}{E}_{N}\ensuremath{\mid}∕N$, increases and approaches a constant value. For all the field strengths considered in this paper, hydrogen, helium, and carbon molecules are found to be bound relative to individual atoms (although for $B$ less than a few $\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.3em}{0ex}}\mathrm{G}$, carbon molecules are very weakly bound relative to individual atoms). Iron molecules are not bound at $B\ensuremath{\lesssim}{10}^{13}\phantom{\rule{0.3em}{0ex}}\mathrm{G}$, but become energetically more favorable than individual atoms at larger field strengths.

Effect of isovector-scalar meson on neutron-star matter in strong magnetic fields

Within the mean-field approximation to the Lagrangian field theory, we study the effects of isovector-scalar meson δ on nucleon effective masses and the equation of state (EOS) of neutron-star matter in strong magnetic fields. We find that the δ-field leads to a large splitting of proton and neutron effective masses in neutron-star matter. The strength of the δ-field decreases, however, with the increase of the magnetic field and is near zero at ultrastrong field. Although the proton effective mass is found to be highly influenced by magnetic fields, the effect of magnetic fields on the neutron effective mass is negligible. The EOS of neutron-star matter turns out to be stiffer at B < 1015 G but becomes softer at stronger magnetic field after including the δ-field. The effect due to the anomalous magnetic moments of both nucleons and lepton is also studied and is found to be appreciable only at ultrastrong magnetic field (B > 1019 G). In the range of 1015–1018 G, the properties of neutron-star matter remain similar to those without magnetic fields.

Interwell exciton dispersion engineering, coherent phonons generation and optical detectionof exciton condensate

AbstractThis issue's Editor's Choice [1] discusses interwell excitons in coupled quantum wells as a candidate for observation of different phases in an exciton system, including the very interesting phenomenon of Bose condensation.The cover picture shows schematically how the generation of coherent phonons and the angular distribution of the exciton photoluminescence (PL) from the quantum well system can be controlled by the external electric and magnetic fields.The first author, Yurii E. Lozovik, is head of the Laboratory of Spectroscopy of Nanostructures at the Institute of Spectroscopy and also Professor of Physics at the Moscow Physical and Technical Institute. His main interests are electron and electron–hole systems in nanostructures, cluster physics, quantum electrodynamics in a cavity, matter in strong magnetic fields, nanotechnology, ultrafast and near field optics, and computer simulations.