A Deterministic Solver for the Langevin Boltzmann Equation Including the Pauli Principle

摘要

A deterministic solver for the Langevin Boltzmann equation including the Pauli principle is presented based on a spherical harmonics expansion. The solver can handle rare events, slow processes and low frequencies without problems and without an increase in CPU time in contrast to the Monte Carlo method. This is demonstrated for strongly degenerate systems and deep traps. Although the two electron sub-ensembles for the different spin directions are correlated due to the deep traps, the spin variable can be eliminated without any approximations resulting in a reduction of the number of unknowns by two. Approximations for the inclusion of the Pauli principle are investigated and found to be so bad that it is better to neglect the Pauli principle than to use those approximations.