A Markovian kinetic equation approach to electron transport through a quantum dot coupled to superconducting leads

We present a derivation of the Markovian master equation for an out-of-equilibrium quantum dot connected to two superconducting reservoirs, which are described by the Bogoliubov-de Gennes Hamiltonians and have the chemical potentials, the temperatures, and the complex order parameters as the relevant quantities. We consider a specific example in which the quantum dot is represented by the Anderson impurity model and study the transport properties, proximity effect and Andreev bound states in equilibrium as well as far-from-equilibrium setups.