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1. Magnetic Dual Chiral DensityWave: A Candidate Quark Matter Phase for the Interior of Neutron Stars

   Efrain J Ferrer and Vivian de la Incera ( November 2021 , Universe)

   MDPI (Ed.)

   In this review, we discuss the physical characteristics of the magnetic dual chiral density wave (MDCDW) phase of dense quark matter and argue why it is a promising candidate for the interior matter phase of neutron stars. The MDCDW condensate occurs in the presence of a magnetic field. It is a single-modulated chiral density wave characterized by two dynamically generated parameters: the fermion quasiparticle mass m and the condensate spatial modulation q. The lowest-Landau-level quasiparticle modes in the MDCDW system are asymmetric about the zero energy, a fact that leads to the topological properties and anomalous electric transport exhibited by this phase. The topology makes the MDCDW phase robust against thermal phonon fluctuations, and as such, it does not display the Landau–Peierls instability, a staple feature of single-modulated inhomogeneous chiral condensates in three dimensions. The topology is also reflected in the presence of the electromagnetic chiral anomaly in the effective action and in the formation of hybridized propagating modes known as axion-polaritons. Taking into account that one of the axion-polaritons of this quark phase is gapped, we argue how incident g-ray photons can be converted into gapped axion-polaritons in the interior of a magnetar star in the MDCDW phase leading the star to collapse, a phenomenon that can serve to explain the so-called missing pulsar problem in the galactic center. 

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2. Magnetic Dual Chiral Density Wave: A Candidate Quark Matter Phase for the Interior of Neutron Stars

   https://doi.org/doi.org/ 10.3390/universe7120458  

   Ferrer, Efrain J. ; Incera, Vivian ( November 2021 , Universe)

   MDPI (Ed.)

   In this review, we discuss the physical characteristics of the magnetic dual chiral density wave (MDCDW) phase of dense quark matter and argue why it is a promising candidate for the interior matter phase of neutron stars. The MDCDW condensate occurs in the presence of a magnetic field. It is a single-modulated chiral density wave characterized by two dynamically generated parameters: the fermion quasiparticle mass m and the condensate spatial modulation q. The lowest- Landau-level quasiparticle modes in the MDCDW system are asymmetric about the zero energy, a fact that leads to the topological properties and anomalous electric transport exhibited by this phase. The topology makes the MDCDW phase robust against thermal phonon fluctuations, and as such, it does not display the Landau–Peierls instability, a staple feature of single-modulated inhomogeneous chiral condensates in three dimensions. The topology is also reflected in the presence of the electromagnetic chiral anomaly in the effective action and in the formation of hybridized propagating modes known as axion-polaritons. Taking into account that one of the axion-polaritons of this quark phase is gapped, we argue how incident γ-ray photons can be converted into gapped axion-polaritons in the interior of a magnetar star in the MDCDW phase leading the star to collapse, a phenomenon that can serve to explain the so-called missing pulsar problem in the galactic center 

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3. Photon propagation in magnetized dense quark matter. A possible solution for the missing pulsar problem.

   https://doi.org/10.1088/1742-6596/2536/1/012005  

   Ferrer, Efrain J ( June 2023 , Journal of Physics: Conference Series)

   Abstract In this paper it is reviewed the topological properties and possible astrophysical consequences of a spatially inhomogeneous phase of quark matter, known as the Magnetic Dual Chiral Density Wave (MDCDW) phase, that can exist at intermediate baryon density in the presence of a magnetic field. Going beyond mean-field approximation, it is shown how linearly polarized electromagnetic waves penetrating the MDCDW medium can mix with the phonon fluctuations to give rise to two hybridized modes of propagation called as axion polaritons because of their similarity with certain modes found in condensed matter for topological magnetic insulators. The formation of axion polaritons in the MDCDW core of a neutron star can serve as a mechanism for the collapse of a neutron star under the bombardment of the gamma rays produced during gamma ray bursts. This mechanism can provide a possible solution to the missing pulsar problem in the galactic center. 

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4. Can the MDCDW condensate withstand the heat of a cold neutron star?

   https://doi.org/10.1088/1742-6596/2536/1/012004  

   Gyory, W. ( June 2023 , Journal of Physics: Conference Series)

   Abstract The correct description of strongly interacting matter at low temperatures and moderately high densities—in particular the conditions realized inside neutron stars—is still unknown. We review some recent results on the magnetic dual chiral density wave (MDCDW) phase, a candidate phase of quark matter for this region of the QCD phase diagram. We highlight the effects of magnetic fields and temperature on the condensate, which can be explored using a high-order Ginzburg-Landau (GL) expansion. We also explain how the condensate’s nontrivial topology, which arises due to the asymmetry in the lowest Landau level modes, affects its physical properties. Finally, we comment on the possible relevance of these results to neutron star applications. Over a wide range of densities and magnetic field strengths, MDCDW is preferred over the chirally symmetric ground state at temperatures consistent with typical cold neutron stars, and in some cases, even hot ones. 

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5. Phase transitions and resilience of the magnetic dual chiral density wave phase at finite temperature and density

   https://doi.org/https://doi.org/10.1103/PhysRevD.106.016011  

   William Gyory and Vivian de la Incera ( July 2022 , Physical review and Physical review letters index)

   We study the phase transitions at finite temperature and density of the magnetic dual chiral density wave (MDCDW) phase. This spatially inhomogeneous phase emerges in cold, dense QCD in the presence of a strong magnetic field. Starting from the generalized Ginzburg-Landau (GL) expansion of the free energy, we derive several analytical formulas that enable fast numerical computation of the expansion coefficients to arbitrary order, allowing high levels of precision in the determination of the physical dynamical parameters, as well as in the transition curves in the temperature vs chemical potential plane at different magnetic fields. At magnetic fields and temperatures compatible with neutron star (NS) conditions, the MDCDW remains favored over the symmetric ground state at all densities. The phase’s “resilience” manifests in (1) a region of small but nonzero remnant mass and significant modulation at intermediate densities, originating in part from the nontrivial topology of the lowest Landau level, and (2) a region of increasing condensate parameters at high densities. Our analysis suggests the MDCDW condensate remains energetically favored at densities and temperatures much higher than previously considered, opening the possibility for this phase to be a viable candidate for the matter structure of even young neutron stars produced by binary neutron star (BNS) mergers. 

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