Schwinger-Keldysh approach to tunneling transport at a hadron-quark interface

We theoretically discuss quantum tunneling transport and frictions at a hadron-quark matter interface based on the Schwinger-Keldysh approach combined with the tunneling Hamiltonian, which has been developed in the context of condensed-matter physics. In the inner core of massive neutron stars, it is expected that cold quark matter appears at sufficiently high densities and hence exhibits color superconductivity, surrounded by nucleon superfluids at lower densities. The perturbative expressions of the tunneling current and the friction at the interface are obtained in terms of the nonequilibrium Green's functions. We demonstrate the dc Josephson current that occurs at the hadron-quark superfluid interface in the present scheme. Our framework can be applied to various conflagrations involving the interfaces relevant to astrophysical phenomena.