Transport Properties in Magnetized Compact Stars

Transport properties of dense quark matter are discussed in the strong magnetic field, B. B dependence as well as density dependence of the Hall conductivity is discussed, based on the microscopic Kubo formula. We took into account the possibility of the inhomogeneous chiral phase at moderate densities, where anomalous Hall effect is intrinsic and resembles the one in Weyl semimetals in condensed matter physics. Some theoretical aspects inherent in anomalous Hall effect are also discussed.

Dissipative Dynamics of Non-Interacting Fermion Systems and Conductivity

In this paper, Non-Equilibrium Steady State that is induced by electric field and the conductivity of non-interacting fermion systems under the dissipative dynamics is discussed. The dissipation is taken into account within a framework of the quantum dynamical semigroup introduced by Davies (1977). We obtain a formula of the conductivity for the stationary state, which is applicable to arbitrary potentials. Our formula gives a justification of an adiabatic factor that is often introduced in practical calculation while using the Kubo formula. In addition, the conductivity of crystals (i.e., periodic potentials) is also discussed.

Transport Properties in Dense QCD Matter

Transport properties of dense QCD matter are discussed. Using the Kubo formula for conductivity, we discuss some topological aspects of quark matter during the chiral transition. The close relation to Weyl semimetal is pointed out and anomalous Hall effect is demonstrated to be possible. In particular, it is shown that the spectral asymmetry of the quasi-particles plays an important role for the Hall conductivity in the magnetic field.