  Non-Markovian quantum state diffusion (NMQSD) provides a powerful approach to
the dynamics of an open quantum system in bosonic environments. Here we develop
an NMQSD method to study the open quantum system in fermionic environments.
This problem involves anticommutative noise functions (i.e., Grassmann
variables) that are intrinsically different from the noise functions of bosonic
baths. We obtain the NMQSD equation for quantum states of the system and the
non-Markovian master equation. Moreover, we apply this NMQSD method to single
and double quantum-dot systems.
