Abstract
We have pointed out the possibilities of quantum Hall effect (QHE) and Shubnikov-de Haas (SdH) oscillation in the transportation of strongly magnetized degenerate quark matter- expected inside the highly dense compact star, such as the neutron star. The anisotropic pattern of electrical conductivity and resistivity tensor is explored in classical to quantum cases by considering the Landau quantization of quarks in the presence of a finite magnetic field. With increasing magnetic field, classical to quantum transitions are realized through enhanced (reduced) resistivity (conductivity) with QHE/SdH type oscillatory patterns. Estimating QCD relaxation time for degenerate quark matter from Ref. [57], eB≈(1−4)mπ2 can be considered a strong magnetic field for massless and degenerate quark matter with quark chemical potential μ≈0.2−0.4 GeV. We discovered exotic quantum magnetic oscillating patterns associated with the QHE and SdH phenomena within the mentioned regimes.
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