Green's Functions Investigations in Quantum Transport Geometries

Sammanfattning: In this thesis we employ the non-equilibrium Green’s function (NEGF) method to study both finite and infinite systems. We develop a codebase capable of computing the steady state interacting NEGF in open systems, i.e. tight-binding leads contacting a central region, in both Hartree-Fock (HF) and second Born (2B) approximations of particle-particle interactions. Furthermore, we use the exact interacting Green’s function on finite re- gions to assess a method we found to compute any pair-correlation function. The method utilizes the Hellman-Feynman theorem applied to the Galitskii- Migdal formula for the total energy of a system. We find that it works well for finite systems, with and without currents, whereas for open (infinite) systems the method requires more care. Lastly, we briefly investigate a non- perturbative G1-G2 scheme; whether computing the two-particle Green’s function in a subsystem approximates the full two-particle Green’s function well. We find that the considered G1-G2 scheme provides results of variable accuracy, suggesting that our investigation is not exhaustive, and that the roles of system geometry and particle density should be further assessed.