Anomalous spontaneous induction of magnetic and electric fields in dense quark matter
In this paper, we will demonstrate that a dense quark-matter system in the dual chiral density wave (DCDW) phase behaves as a ferromagnet in the sense that its magnetic-field dependent magnetization remains different from zero even at $B\rightarrow 0$. The corresponding permanent magnetization is a function of the baryonic chemical potential $μ$, decreasing up to zero as $μ$ increases in the range of intermediate densities ($312$ MeV $\leqslant μ\leqslant 342$ MeV) and then increasing from zero in the higher density interval $490$ MeV$\leqslant μ\leqslant 550$ MeV. We will show that this system's ability to generate permanent magnetization, together with the existence of the axial anomaly, open up the possibility of spontaneously generating a magnetic field coupled to a collinear electric field. The generated magnetic field can reach values up to $10^{16}$ G, depending on $μ$, and the electric field will be 3 orders smaller. The fact that the DCDW phase is able to induce a magnetic field can be seen as its spontaneous tendency to remove the so called Landau-Peierls instability that is present in this single-modulated phase in the absence of a magnetic field. The spontaneous induction of a strong magnetic field at intermediate to high densities can be of interest for the astrophysics of compact stellar objects exhibiting strong magnetic fields as magnetars.