Abstract
Several anomalous electromagnetic effects that can take place in quark matter at low temperatures and intermediate densities will be discussed. The anomalous transport properties of the spatially inhomogeneous phase of quark matter known as the Magnetic Dual Chiral Density Wave (MDCDW) phase will be reviewed. Going beyond mean-field approximation, it will be shown how linearly polarized electromagnetic waves that penetrate the MDCDW medium mix with the phonon fluctuations to give rise to two hybridized modes of propagation called axion polaritons. Finally, some possible implications of these results for the astrophysics of neutron stars will be indicated.
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