  The Lindblad equation is commonly used for studying quantum dynamics in open
systems that cannot be completely isolated from an environment, relevant to a
broad variety of research fields, such as atomic physics, materials science,
quantum biology and quantum information and computing. For electrons in
condensed matter systems, the Lindblad dynamics is intractable even if their
mutual Coulomb repulsion could somehow be switched off. This is because they
would still be able to affect each other by interacting with the bath. Here, we
develop an approximate approach, based on the Hubbard-Stratonovich
transformation, which allows to evolve non-interacting Fermions in open quantum
systems. We discuss several applications for systems of trapped 1D Fermions
showing promising results.
