General analytical solution to exact fermion master equation

TL;DR

This paper presents a comprehensive analytical solution to the exact fermion master equation, enabling detailed study of quantum dynamics in fermionic systems with arbitrary initial states and multiple orbitals.

Contribution

It provides the first general analytical solution to the fermion master equation in particle number representation for systems with any number of orbitals.

Findings

Demonstrates the solution's application to nanostructured artificial molecules.

Shows how different initial states affect transient dynamics.

Reveals multiple transition pathways in fermionic quantum systems.

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.