General analytical solution to exact fermion master equation

Abstract

The exact fermion master equation previously obtained in [Phys. Rev. B \textbf{78}, 235311 (2008); New J. Phys. \textbf{12}, 083013 (2010)] describes the dynamics of quantum states of a principal system of fermionic particles under the influences of external fermion reservoirs (e.g. nanoelectronic systems). Here, we present the general solution to this exact fermion master equation. The solution is analytically expressed in the most intuitive particle number representation. It is applicable to an arbitrary number of orbitals in the principal system prepared at arbitrary initial states. We demonstrate the usefulness of such general solution with the transient dynamics of nanostructured artificial molecules. We show how various initial states can lead to distinct transient dynamics, manifesting a multitude of underlying transition pathways.