How electronic dynamics with Pauli exclusion produces Fermi-Dirac statistics

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Computational chemistry

Background:

• Accurate long-time population distributions are crucial for dynamics methods.
• Existing methods may not correctly capture equilibrium states for electron-bath systems.

Purpose of the Study:

• Derive a one-body reduced density matrix dynamics for electrons in contact with a bath.
• Develop a method that ensures proper relaxation to equilibrium distributions.
• Generalize Redfield theory for many-electron systems.

Main Methods:

• Derivation of an equation of motion for the electron density matrix.
• Application of time-dependent perturbation theory and extended normal ordering.
• Numerical applications to molecules and atomic chains.

Main Results:

• The derived equation of motion shows electron transition rates depend on the density matrix.
• Hole blocking factors lead to Fermi-Dirac distribution instead of Boltzmann.
• Relaxation rates are not constant due to blocking effects.
• Dephasing and relaxation are important for atomic chains.

Conclusions:

• The new dynamics method correctly approaches equilibrium population distributions.
• The method generalizes Redfield theory and ensures orbital occupations remain physically realistic.
• The derived equations are applicable to various molecular and condensed matter systems.