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Title: How electronic dynamics with Pauli exclusion produces Fermi-Dirac statistics

It is important that any dynamics method approaches the correct population distribution at long times. In this paper, we derive a one-body reduced density matrix dynamics for electrons in energetic contact with a bath. We obtain a remarkable equation of motion which shows that in order to reach equilibrium properly, rates of electron transitions depend on the density matrix. Even though the bath drives the electrons towards a Boltzmann distribution, hole blocking factors in our equation of motion cause the electronic populations to relax to a Fermi-Dirac distribution. These factors are an old concept, but we show how they can be derived with a combination of time-dependent perturbation theory and the extended normal ordering of Mukherjee and Kutzelnigg for a general electronic state. The resulting non-equilibrium kinetic equations generalize the usual Redfield theory to many-electron systems, while ensuring that the orbital occupations remain between zero and one. In numerical applications of our equations, we show that relaxation rates of molecules are not constant because of the blocking effect. Other applications to model atomic chains are also presented which highlight the importance of treating both dephasing and relaxation. Finally, we show how the bath localizes the electron density matrix.
Authors:
; ;  [1]
  1. Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556 (United States)
Publication Date:
OSTI Identifier:
22415602
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 13; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMIC MODELS; CHANNELING; DENSITY MATRIX; ELECTRON DENSITY; ELECTRONS; EQUATIONS OF MOTION; FERMI STATISTICS; HOLES; KINETIC EQUATIONS; MOLECULES; PERTURBATION THEORY; RELAXATION; TIME DEPENDENCE