Electron transport through a mesoscopic hybrid multiterminal resonant-tunneling system

For a mesoscopic hybrid system which contains a normal central region coupl ed to multiple superconducting leads, a general expression of the current i s derived by using nonequilibrium-Green-function method. This current formu la can be used to describe the case with time-dependent external fields app lied to any parts of the system, arbitrarily finite voltages, and any kinds of interactions in the central region. For a normal two-terminal interacti ng electron system, this expression reduces to the general time-dependent c urrent formula previously obtained by Wingreen et al. [Phys. Rev. B 98, 848 7 (1993)]. As an application, we use this current formula to study a specia l case of a noninteracting single-level central region coupled to two or th ree superconducting leads, respectively.