Master equation for the Wigner function of normal and superconducting single-electron transistors

We have derived a master equation for the Wigner function that describes charge dynamics of normal and superconducting single-electron transistors in a unified way. In the case of a normal single-electron transistor, the master equation for the Wigner function is equivalent to that of the so-called orthodox theory. For a superconducting single-electron transistor, the tunneling rates consist of three parts: quasiparticle tunneling, quasiparticle-pair tunneling, and Cooper-pair tunneling. Conditions of the Coulomb blockade of quasiparticle tunneling are examined.