How Electronic Dynamics with Pauli Exclusion Produces Fermi-Dirac Statistics

摘要

It is important that any dynamics method approaches the correct populationdistribution at long times. In this paper, we derive a one-body reduced densitymatrix dynamics for electrons in energetic contact with a bath. We obtain aremarkable equation of motion which shows that in order to reach equilibriumproperly, rates of electron transitions depend on the density matrix. Eventhough the bath drives the electrons towards a Boltzmann distribution, holeblocking factors in our equation of motion cause the electronic populations torelax to a Fermi-Dirac distribution. These factors are an old concept, but weshow how they can be derived with a combination of time-dependent perturbationtheory, and the extended normal ordering of Mukherjee and Kutzelnigg. Theresulting non-equilibrium kinetic equations generalize the usual Redfieldtheory to many-electron systems, while ensuring that the orbital occupationsremain between zero and one. In numerical applications of our equations, weshow that relaxation rates of molecules are not constant because of theblocking effect. Other applications to model atomic chains are also presentedwhich highlight the importance of treating both dephasing and relaxation.Finally we show how the bath localizes the electron density matrix.